feat: add Triple.post_imp_elim and Triple.rotate_pre#14034
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This PR adds two Hoare triple lemmas to `Std.Do`. `Triple.post_imp_elim` eliminates an implication in the postcondition: a specification `⦃P⦄ x ⦃Q⦄` upgrades a proof of `⦃P⦄ x ⦃Q →ₚ R⦄` to `⦃P⦄ x ⦃R⦄`. `Triple.rotate_pre` proves a triple for `prog` from a specification of an observation `p` by rotating `p` into program position with the goal `wp⟦prog⟧ Post` as its postcondition, so that `mvcgen` can step through `p`. This supports specifications written in the object language, where a programmatic precondition such as `(pre x).holds` appears as a triple hypothesis. The premise `hp` of `rotate_pre` states that successful runs of `p` leave the state unchanged; it holds for every program of a stateless monad such as `Except`. Tests exercise the pattern for unfoldable and opaque `Except` programs.
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This PR adds two Hoare triple lemmas to
Std.Do.Triple.post_imp_elimeliminates an implication in the postcondition: a specification⦃P⦄ x ⦃Q⦄upgrades a proof of⦃P⦄ x ⦃Q →ₚ R⦄to⦃P⦄ x ⦃R⦄.Triple.rotate_preproves a triple forprogfrom a specification of an observationpby rotatingpinto program position with the goalwp⟦prog⟧ Postas its postcondition, so thatmvcgencan step throughp.This supports specifications written in the object language, where a programmatic precondition such as
(pre x).holdsappears as a triple hypothesis. The premisehpofrotate_prestates that successful runs ofpleave the state unchanged; it holds for every program of a stateless monad such asExcept. Tests exercise the pattern for unfoldable and opaqueExceptprograms.