Note that $S$ is a closed point of $\tilde{\mathfrak{X}}^{\prime}$ and hence proper over $\tilde{K}$. Therefore also $Y$ is proper over $\tilde{K}$ since it is a closed subset of $\tilde{\iota}^{-1}(S)$ and $\iota$ is proper by [Tem00, Corollary 4.4]. Let $D$ be the Cartier divisor on $\mathfrak{X}^{\prime\prime}$ induced by $h$ as in Proposition 2.11 such that $c_{1}\left(\mathcal{O}(h\circ p_{\mathfrak{X}^{\prime}})\right)^{n}.Y=D^{n}.Y$. We show by induction that for all $0\leq l\leq n$ there is a strata cycle $Y_{l}$ of dimension $n-l$ whose components are contained in $Y$ such that $\Deg(D^{n}.Y)=\Deg(D^{n-l}.Y_{l})$. The case $l=0$ is clear by taking $Y_{0}:=Y$. Now let $l<n$ and $Y_{l}$ be as claimed. Let $Y^{\prime}$ be a stratum of $Y_{l}$, such that $Y^{\prime}$ is associated to an $l$-dimensional open face $\tau^{\prime}$ of $\mathfrak{D}$, i.e. $Y^{\prime}=\red_{\mathfrak{X}^{\prime\prime}}(p_{\mathfrak{X}^{\prime\prime}}^{-1}(\tau^{\prime}))$ with $u\in\overline{\tau^{\prime}}$ by the stratum face correspondence (Proposition 2.8). Using $\tau^{\prime}\subseteq\tau\subseteq\mathbb{R}^{n}$, there is an affine linear function $a:\mathbb{R}^{n}\rightarrow\mathbb{R}$ such that $h\Big|_{\tau^{\prime}}=a\Big|_{\tau^{\prime}}$. Then $h-a\Big|_{\tau}$ defines a Cartier divisor $D_{Y^{\prime}}$ on $\mathfrak{X}^{\prime\prime}$ by Proposition 2.11 which is numerically equivalent to $D$ on $Y$ by Lemma 2.13 and which is trivial on $Y^{\prime}$ because $h-a\Big|_{\tau^{\prime}}=0$. Hence, as $\overline{Y^{\prime}}$ is a strata subset, $D_{Y^{\prime}}.\overline{Y^{\prime}}$ is a strata cycle. Write $Y_{l}=\sum_{Y^{\prime}}m_{Y^{\prime}}\overline{Y^{\prime}}$ where the sum ranges over a finite number of $n-l$-dimensional strata of $\tilde{\mathfrak{X}}^{\prime\prime}$ contained in $Y$. Then we can calculate:

	$\displaystyle\Deg(D^{n}.Y)$	$\displaystyle=\Deg\left(D^{n-l}.Y_{l}\right)$
		$\displaystyle=\Deg\left(D^{n-l}.\sum_{Y^{\prime}}m_{Y^{\prime}}\overline{Y^{\prime}}\right)$
		$\displaystyle=\Deg\left(\sum_{Y^{\prime}}m_{Y^{\prime}}D^{n-l}.\overline{Y^{\prime}}\right)$
		$\displaystyle=\Deg\left(\sum_{Y^{\prime}}m_{Y^{\prime}}D^{n-l-1}.(D_{Y^{\prime}}.\overline{Y^{\prime}})\right)$
		$\displaystyle=\Deg\left(D^{n-l-1}.\sum_{Y^{\prime}}m_{Y^{\prime}}D_{Y^{\prime}}.\overline{Y^{\prime}}\right)$

and $Y_{l+1}:=\sum_{Y^{\prime}}m_{Y^{\prime}}D_{Y^{\prime}}.\overline{Y^{\prime}}$ is a strata cycle as claimed. We use this for $l=n$ to see that $\Deg(D^{n}.Y)=\Deg(Y_{n})$ for a strata cycle $Y_{n}$ of dimension $0$ contained in $Y$. Its components are strata points $S_{i}$ of $\mathfrak{X}^{\prime\prime}$ which are mapped by $\iota$ to the point $S$ corresponding to $\tau$. Now let $\mathfrak{U}^{\prime}\subseteq\mathfrak{X}^{\prime}$ be a formal open subset with an étale morphism $\psi:\mathfrak{U}^{\prime}\rightarrow\mathfrak{X}(\boldsymbol{n},\boldsymbol{a})$ such that $S$ is the distinguished stratum of $\mathfrak{U}^{\prime}$ (cf. Proposition 2.5) and define $\mathfrak{U}^{\prime\prime}:=\iota^{-1}(\mathfrak{U}^{\prime})$. Note that there is no factor $\mathfrak{X}(m)$ because $\tau$ is of maximal dimension. As the strata occurring in the intersection process correspond to open faces of $\mathfrak{D}$ with vertex $u$, their intersection with $\mathfrak{U}^{\prime\prime}$ is nonempty. Hence we may calculate the multiplicities of $Y_{n}$ locally on $\mathfrak{U}^{\prime\prime}$. The stratification of $\tilde{\mathfrak{U}}^{\prime\prime}$ is obtained by the preimages of the strata of $\tilde{\mathfrak{X}}(\boldsymbol{n},\boldsymbol{a})^{\prime}$ (see proof of Proposition 2.8) with respect to the base change $\psi^{\prime}:\mathfrak{U}^{\prime\prime}\rightarrow\mathfrak{X}(\boldsymbol{n},\boldsymbol{a})^{\prime}$ of $\psi$ (cf. Construction 2.6). Let $Y_{u}=\overline{\tilde{\psi}^{\prime}(\tilde{\mathfrak{U}}^{\prime\prime}\cap Y)}$ be the irreducible component in $\tilde{\mathfrak{X}}(\boldsymbol{n},\boldsymbol{a})^{\prime}$ corresponding to $u$ and $D_{u}$ the Cartier divisor on $\mathfrak{X}(\boldsymbol{n},\boldsymbol{a})^{\prime}$ whose pullback gives the Cartier divisor $D$ associated to $h$ on $\mathfrak{U}^{\prime\prime}$ (cf. proof of Proposition 2.11). By applying the modifications of $D$ in the induction step also to $D_{u}$ we obtain a strata cycle $Y_{n}^{t}=\sum m_{j}P_{j}$ of $\tilde{\mathfrak{X}}(\boldsymbol{n},\boldsymbol{a})^{\prime}$ whose pullback is $Y_{n}$ (as the intersection product is compatible with flat pullback by [Ful98, Proposition 2.3(d)]) and which has the same degree as $D_{u}^{n}.Y_{u}$ using Lemma 2.13. Now let

	$\displaystyle\val:(\mathbb{G}_{m}^{\boldsymbol{n}})_{K}^{\textup{an}}$	$\displaystyle\rightarrow\mathbb{R}^{\boldsymbol{n}},$
	$\displaystyle q$	$\displaystyle\mapsto(-\log q(x_{01}),...,-\log q(x_{0n_{0}}),...,-\log q(x_{p1}),...,-\log q(x_{pn_{p}}))$

and $\Sigma:=\left\{\boldsymbol{w}\in\mathbb{R}_{\geq 0}^{\boldsymbol{n}}\;\Big|\;w_{i1}+...+w_{in_{i}}\leq v(a_{i}),0\leq i\leq p\right\}$. As we have an isomorphism

$$\mathfrak{X}(\boldsymbol{n},\boldsymbol{a})^{\textup{an}}\tilde{\rightarrow}\val^{-1}(\Sigma)$$

and using [Gub13, Corollary 6.15], we find that $Y_{u}$ is a toric variety with fan given by the cones generated by $\Delta^{\prime}-u$ for $\Delta^{\prime}\in\mathfrak{D}$ with vertex $u$ (in fact we identify $\tau$ with $\Sigma$ by forgetting about the coordinate with index $0$ for each $i$). $D_{u}\Big|_{Y_{u}}$ is given up to multiplication by a constant by the divisor $D^{\prime}_{u}$ on $Y_{u}$ associated to the linear function $h^{\prime}:=h(\cdot+u)-h(u)$. By [Ful93, 3.4,5.3] we have

$$\lambda(P_{D^{\prime}_{u}})=\frac{\Deg({D^{\prime}}_{u}^{n}.Y_{u})}{n!},$$

where

$$P_{D^{\prime}_{u}}=\left\{y\in\mathbb{R}^{n}\;\Big|\;\langle z,y\rangle\leq\psi_{D^{\prime}_{u}}(z)=h^{\prime}(z)\;\forall z\in\mathbb{R}^{n}\right\}=\nabla h^{\prime}(0)$$

and $\lambda$ denotes the standard Lebesgue measure. For the last term we get

	$\displaystyle\nabla h^{\prime}(0)$	$\displaystyle=\left\{p\in\mathbb{R}^{n}\;\Big|\;\forall x\in\tau-u\;:\;h^{\prime}(0)+\langle x,p\rangle\leq h^{\prime}(x)\right\}$
		$\displaystyle=\left\{p\in\mathbb{R}^{n}\;\Big|\;\forall x\in\tau-u\;:\;\langle x,p\rangle\leq h(x+u)-h(u)\right\}$
		$\displaystyle=\left\{p\in\mathbb{R}^{n}\;\Big|\;\forall x\in\tau\;:\;h(u)+\langle x-u,p\rangle\leq h(x)\right\}$
		$\displaystyle=\nabla h(u).$

Hence

$$\frac{1}{n!}\Deg(Y_{n}^{t})=\frac{\Deg({D^{\prime}}_{u}^{n}.Y_{u})}{n!}=\lambda(P_{D^{\prime}_{u}})=\lambda(\nabla h(u))=\MA(h)(\{u\}).$$

With $\iota^{\prime}$ denoting the morphism $\mathfrak{X}(\boldsymbol{n},\boldsymbol{a})^{\prime}\rightarrow\mathfrak{X}(\boldsymbol{n},\boldsymbol{a})$ we conclude

$$\Deg(D^{n}.Y)=\Deg\left(Y_{n}\right)=\Deg\left(\psi^{\prime\ast}Y_{n}^{t}\right)=\Deg\left(\iota_{\ast}\psi^{\prime\ast}\sum m_{j}P_{j}\right).$$

Using [Ful98, Proposition 1.7] this equals

$$\Deg\left(\psi^{\ast}\iota^{\prime}_{\ast}\sum m_{j}P_{j}\right)=\Deg\left(\psi^{\ast}\sum m_{j}[P_{j}:\{\tilde{\boldsymbol{0}}\}]\cdot\{\tilde{\boldsymbol{0}}\}\right).$$

As $\psi^{-1}(\{\tilde{\boldsymbol{0}}\})=S$ is reduced since $\psi$ is smooth, this amounts to

$$\Deg\left(\sum m_{j}\Deg(P_{j})S\right)=\Deg(S)\cdot\Deg(Y_{n}^{t})=\Deg(S)\cdot n!\cdot\MA(h)(\{u\}).$$

This yields the equality we wanted to prove. ∎

We already know by Theorem 5.2 that the equation holds on the set of vertices. Furthermore it is clear from the definition, that $c_{1}\left(\overline{\mathcal{O}}^{h\circ p_{\mathfrak{X}^{\prime}}}\right)^{n}$ is supported on the vertices of $\mathfrak{D}$. What remains to show is that this also holds for $\MA(h)$.

Let $U:=\tau\setminus\left\{u\in\tau\;\Big|\;u\text{ is a vertex of }\mathfrak{D}\right\}$. We want to show $\MA(h)(U)=0$. Let $\Delta_{1},...,\Delta_{r}$ be the open faces of $\mathfrak{D}$ of dimension at least one. For every $j\in\{1,...,r\}$ there is a $v_{j}\in\mathbb{R}^{n}\setminus\{0\}$ such that for all $y\in\Delta_{j}$ there exists $\epsilon\in\mathbb{R}_{+}$ such that $y\pm\epsilon v_{j}\in\Delta_{j}$. Furthermore $h_{j}:=h\Big|_{\Delta_{j}}=\boldsymbol{m}_{j}\boldsymbol{x}+v(\alpha_{j})$ for some $\boldsymbol{m}_{j}\in\mathbb{Z}^{n}$ and $\alpha_{j}\in K^{\times}$ and we define $h_{j}^{lin}:=\boldsymbol{m}_{j}\boldsymbol{x}$. Now let $y\in U$. Then there is an $i$ such that $y\in\Delta_{i}$. For $p\in\nabla h(y)$ and $\epsilon$ as above it follows

	$\displaystyle\epsilon\langle v_{i},p\rangle$	$\displaystyle=h_{i}(y)+\langle y+\epsilon v_{i}-y,p\rangle-h_{i}(y)$
		$\displaystyle\leq h_{i}(y+\epsilon v_{i})-h_{i}(y)$
		$\displaystyle=h_{i}^{lin}(\epsilon v_{i})$
		$\displaystyle=\epsilon h_{i}^{lin}(v_{i}),$

hence

$$\langle v_{i},p\rangle\leq h_{i}^{lin}(v_{i}).$$

A similar argument shows

$$-\epsilon\langle v_{i},p\rangle\leq-\epsilon h_{i}^{lin}(v_{i})$$

and hence

$$\langle v_{i},p\rangle\geq h_{i}^{lin}(v_{i}).$$

We conclude $\langle v_{i},p\rangle=h_{i}^{lin}(v_{i})$ and $p$ lies in a hypersurface which depends on $i$ but not on $y$. Hence $\bigcup_{y\in U}\nabla h(y)$ is contained in the union of $r$ hypersurfaces. Therefore

$$\MA(h)(U)=\lambda\left(\bigcup_{y\in U}\nabla h(y)\right)=0,$$

∎

Let $y\in p_{\mathfrak{X}}^{-1}(\tau)$ and $x:=p_{\mathfrak{X}}(y)\in\tau$. There is an open neighbourhood $U$ of $x$ in $\tau$ such that we can write $h\Big|_{U}=\max_{i=1,...,s}h_{i}\Big|_{U}$ for suitable rational affine linear functions $h_{i}$ on $\tau$. After passing to some multiple, each $h_{i}$ induces a formal metric on $\mathfrak{X}^{\prime an}$ by Proposition 2.11 where $\mathfrak{X}^{\prime}$ is defined as in Remark 5.1. Therefore the $h_{i}$ induce piecewise $\mathbb{Q}$-linear metrics on $\mathcal{O}_{\mathfrak{X}^{\textup{an}}}\Big|_{p_{\mathfrak{X}}^{-1}(\tau)}$ since $p_{\mathfrak{X}}^{-1}(\tau)\subseteq\mathfrak{X}^{\prime an}$. Hence in the neighbourhood $p_{\mathfrak{X}}^{-1}(U)$ of $y$, the metric induced by $h$ is given as the minimum of the metrics corresponding to the $h_{i}$, which are semipositive at $y$ by Lemma 2.13. Indeed let $(\mathfrak{X}^{\prime\prime}_{i},\mathfrak{L}_{i})$ be a formal model of the trivial bundle associated to $h_{i}$ as obtained by Proposition 2.11. Then by [GK19, Proposition 6.5] (the proof of the implication we need does neither use that $K$ is algebraically closed nor that the generic fibre is algebraic) it is enough to show that $\Deg_{\mathfrak{L}_{i}}(Y)\geq 0$ for any closed curve $Y$ in $\tilde{\mathfrak{X}}^{\prime\prime}_{i}$ with $Y\subseteq\red(p_{\mathfrak{X}^{\prime\prime}_{i}}^{-1}(\tau))$ but by Lemma 2.13 we even have equality. Now we extend the metrics induced by the $h_{i}$ from a compact strictly $K$-analytic neighbourhood of $y$ to $X^{\textup{an}}$ by [GM19, Proposition 2.7] and then it follows from Proposition 3.11 that $||\cdot||$ is semipositive at $y$. ∎

We can cover $\tau$ by polytopes $(\Delta_{m})_{m\in\mathbb{N}}$ such that $\Delta_{m-1}\subseteq\Delta_{m}$. By [BPS14, Proposition 2.5.24] for each $m$ there is a family of rational piecewise affine linear convex functions $(h_{i}^{m})_{i\in\mathbb{N}}$ on $\Delta_{m}$ converging uniformly to $h\Big|_{\Delta_{m}}$ (note that after normalization we can assume that $\mathbb{Z}$ is contained in the value group of $K$). We extend these functions to rational piecewise affine linear convex functions on $\overline{\tau}$. Then by Proposition 5.6 the metrics induced by the $h_{i}^{m}$ are semipositive piecewise $\mathbb{Q}$-linear metrics on $p_{\mathfrak{X}}^{-1}(\tau)$ which implies that the metric induced by $h\Big|_{\Delta_{m}}$ is semipositive. By Corollary 5.5 we have

$$c_{1}\left(\overline{\mathcal{O}}^{h_{i}^{m}\circ p_{\mathfrak{X}}}\right)^{n}=\Deg(S)\cdot n!\cdot\MA(h_{i}^{m})$$

for every $m,i\in\mathbb{N}$. Denoting the interior of $\Delta_{m}$ by $\Delta_{m}^{\circ}$ and using Proposition 4.13 we find that for fixed $m$ the left hand side converges to $c_{1}\left(\overline{\mathcal{O}}^{h\circ p_{\mathfrak{X}}}\right)^{n}$ on $p_{\mathfrak{X}}^{-1}(\Delta_{m}^{\circ})$. The right hand side converges to $\Deg(S)\cdot n!\cdot\MA(h)$ on $\Delta_{m}^{\circ}$ by continuity of the real Monge-Ampère operator. As this holds for any $m$ and the $\Delta_{m}$ cover $\tau$ this proves the corollary. ∎

Let $\mathfrak{X}^{\prime}$ be a strongly nondegenerate strictly polystable formal scheme such that there is a surjective étale morphism $\varphi:\mathfrak{X}^{\prime}\rightarrow\mathfrak{X}$. Let $q\in\tilde{\mathfrak{X}}$ be the closed point corresponding to $\tau$. By Proposition 2.4 we have $\red_{\mathfrak{X}}^{-1}(q)=p_{\mathfrak{X}}^{-1}(\tau)$. Choose $q^{\prime}\in\tilde{\mathfrak{X}^{\prime}}$ with $\varphi(q^{\prime})=q$. By [Gub07, Proposition 2.9] we have that $\varphi$ induces an isomorphism $\red_{\mathfrak{X}^{\prime}}^{-1}(q^{\prime})\tilde{\rightarrow}p_{\mathfrak{X}}^{-1}(\tau)$. Hence the pullback of $\left(\mathcal{O}_{X^{\textup{an}}}\Big|_{p_{\mathfrak{X}}^{-1}(\tau)},\|\cdot\|\right)$ is the trivial bundle on $\red_{\mathfrak{X}^{\prime}}^{-1}(q^{\prime})$ endowed with the metric $\|1\|^{\prime}=e^{-h\circ p_{\mathfrak{X}}\circ\varphi}$. Since $p_{\mathfrak{X}}\circ\varphi=\varphi\circ p_{\mathfrak{X}^{\prime}}$ it follows that $\|\cdot\|^{\prime}$ is the metric associated to the function $h\circ\varphi$ on $\tau^{\prime}:=p_{\mathfrak{X}^{\prime}}(\red_{\mathfrak{X}^{\prime}}^{-1}(q^{\prime}))$ which is again rational piecewise affine linear by [Ber04, Theorem 6.1.1] and we may assume it is convex by definition. Let $y\in p_{\mathfrak{X}}^{-1}(\tau)$. In a neighbourhood of $p_{\mathfrak{X}^{\prime}}(y^{\prime})$ where $y^{\prime}\in p_{\mathfrak{X}^{\prime}}^{-1}(\tau^{\prime})$ with $\varphi^{\textup{an}}(y^{\prime})=y$ we can write $h\circ\varphi^{\textup{an}}=\max_{i=1,...,s}h^{\prime}_{i}$ for suitable affine linear functions $h^{\prime}_{i}$ on $\tau^{\prime}$. Now as $\varphi^{\textup{an}}:p_{\mathfrak{X}^{\prime}}^{-1}(\tau^{\prime})\rightarrow p_{\mathfrak{X}}^{-1}(\tau)$ is an isomorphism we have $h=\max_{i=1,...,s}h_{i}$ where $h_{i}$ are the piecewise affine linear functions on $\tau$ satisfying $h^{\prime}_{i}=h_{i}\circ\varphi^{\textup{an}}$. Now the metrics associated to the $h^{\prime}_{i}$ are piecewise $\mathbb{Q}$-linear and semipositive in $y^{\prime}$ by the same argument as in the proof of Proposition 5.6. Hence the piecewise $\mathbb{Q}$-linear metrics associated to the $h_{i}$ extend from a compact strictly $K$-analytic neighbourhood of $y$ to global metrics by [GM19, Proposition 2.7] which are semipositive in $y$. Now as $\|\cdot\|$ is locally around $y$ given as the minimum of these metrics, also $\|\cdot\|$ is a piecewise $\mathbb{Q}$-linear metric which is semipositive in $y$ by Proposition 3.11. ∎

Let $\mathbb{C}_{K}$ be the completion of an algebraic closure of $K$. Then there are exactly $\Deg(S)$ points in the special fibre of $\mathfrak{X}_{\mathbb{C}_{K}}$ mapping to $S$, hence there are precisely $\Deg(S)$ open faces in the skeleton associated to $\mathfrak{X}_{\mathbb{C}_{K}}$ lying over $\tau$. As the base change induces an isomorphism of each of these faces with $\tau$, we have $\iota_{\ast}\MA(\iota^{\ast}h)=\Deg(S)\MA(h)$. Using this and the invariance of the non-archimedean Monge-Ampère measure under base change we may assume $K=\mathbb{C}_{K}$. As in the proof of Proposition 5.9 we choose a strongly nondegenerate strictly polystable formal scheme $\mathfrak{X}^{\prime}$ and a surjective étale morphism $\varphi:\mathfrak{X}^{\prime}\rightarrow\mathfrak{X}$. Let $\tau^{\prime}$ be an open face of the skeleton associated to $\mathfrak{X}^{\prime}$ lying over $\tau$. As we have seen, $\varphi$ induces an isomorphism $p_{\mathfrak{X}^{\prime}}^{-1}(\tau^{\prime})\tilde{\rightarrow}p_{\mathfrak{X}}^{-1}(\tau)$. As in the proof of Corollary 5.7 there is a sequence of rational piecewise affine linear convex functions $(h^{\prime}_{i})_{i\in\mathbb{N}}$ on $\tau^{\prime}$ converging locally uniformly to $h\circ\varphi^{\textup{an}}$. Let $h_{i}$ be the piecewise affine linear functions on $\tau$ such that $h_{i}\circ\varphi^{\textup{an}}=h^{\prime}_{i}$. By Proposition 5.9 the metrics induced by the $h_{i}$ are semipositive piecewise $\mathbb{Q}$-linear metrics on $p_{\mathfrak{X}}^{-1}(\tau)$ which implies that the metric induced by $h$ is locally semipositive. As the restriction of $\varphi$ to $p_{\mathfrak{X}^{\prime}}^{-1}(\tau^{\prime})$ is an isomorphism onto $p_{\mathfrak{X}}^{-1}(\tau)$ we have

$$c_{1}\left(\overline{\mathcal{O}}^{h_{i}\circ p_{\mathfrak{X}}}\right)^{n}=\left(\varphi\Big|_{p_{\mathfrak{X}^{\prime}}^{-1}(\tau^{\prime})}\right)_{\ast}c_{1}\left(\left(\varphi\Big|_{p_{\mathfrak{X}^{\prime}}^{-1}(\tau^{\prime})}\right)^{\ast}\overline{\mathcal{O}}^{h_{i}\circ p_{\mathfrak{X}}}\right)^{n}$$

By Corollary 5.5 we have

$$c_{1}\left(\left(\varphi\Big|_{p_{\mathfrak{X}^{\prime}}^{-1}(\tau^{\prime})}\right)^{\ast}\overline{\mathcal{O}}^{h_{i}\circ p_{\mathfrak{X}}}\right)^{n}=c_{1}\left(\overline{\mathcal{O}}^{h_{i}\circ\varphi^{\textup{an}}\circ p_{\mathfrak{X}^{\prime}}}\right)^{n}=n!\cdot\MA\left(h_{i}\circ\varphi^{\textup{an}}\Big|_{\tau^{\prime}}\right).$$

Hence

$$c_{1}\left(\overline{\mathcal{O}}^{h_{i}\circ p_{\mathfrak{X}}}\right)^{n}=\left(\varphi\Big|_{p_{\mathfrak{X}^{\prime}}^{-1}(\tau^{\prime})}\right)_{\ast}\left(n!\cdot\MA\left(h_{i}\circ\varphi^{\textup{an}}\Big|_{\tau^{\prime}}\right)\right)=n!\cdot\MA(h_{i}).$$

It is easily seen that in Proposition 4.13 we can replace uniform convergence by locally uniform convergence. The claim follows from this fact and continuity of the real Monge-Ampère operator. ∎