@@ -288,7 +288,7 @@ As an example for how to use this adequacy theorem, let us say we wanted to prov
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@@ -288,7 +288,7 @@ As an example for how to use this adequacy theorem, let us say we wanted to prov
\end{cor}
\end{cor}
To prove the conclusion of this corollary, we assume some $\state_0, \vec\obs, \tpool_1, \state_1$ and $([\expr_0], \state_0)\tpsteps[\vec\obs](\tpool_1, \state_1)$, and we instantiate the main theorem with this execution and $\metaprop\eqdef\All\expr\in\tpool_1. \toval(\expr)\neq\bot\lor\red(\expr, \state_1)$.
To prove the conclusion of this corollary, we assume some $\state_0, \vec\obs, \tpool_1, \state_1$ and $([\expr_0], \state_0)\tpsteps[\vec\obs](\tpool_1, \state_1)$, and we instantiate the main theorem with this execution and $\metaprop\eqdef\All\expr\in\tpool_1. \toval(\expr)\neq\bot\lor\red(\expr, \state_1)$.
We can then show the premise of adequacy using the Iris entailment that we assumed in the corollary and:
We can then show the premise of adequacy using the Iris entailment that we assumed in the corollary and:
This proof, just like the following, also exploits that we can freely swap between meta-level universal quantification ($\All x. \TRUE\proves\prop$) and quantification in Iris ($\TRUE\proves\All x. \prop$).
This proof, just like the following, also exploits that we can freely swap between meta-level universal quantification ($\All x. \TRUE\proves\prop$) and quantification in Iris ($\TRUE\proves\All x. \prop$).