feat: add SPred and PostCond entailment lemmas#13582
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This PR adds several entailment-related lemmas to `Std.Do.SPred` and `Std.Do.PostCond`, intended for goal-decomposition during program verification proof automation. - `SPred.down_pure_nil` and `SPred.apply_pure_cons` (existing `rfl` lemmas) become `@[simp, grind =]`. Drops the now-redundant `pure_cons` argument from `simp` in `conjunction_apply`. - New `SPred.entails_nil_intro` and `SPred.entails_nil_pure_intro`: introduction forms for `entails` at `SPred []`, mirroring the existing `entails_cons_intro`. - New `SPred.down_pure_intro`: derive `(pure φ).down` from `φ`. - New `SPred.apply_pure_cons_entails_l`/`_r`: peel a state argument from `pure (σ::σs) φ s` on either side of `⊢ₛ`. - New `Std.Do.ExceptConds.entails.pure`: closes any `⊢ₑ` goal at `PostShape.pure`, where `ExceptConds.entails` reduces to `True`.
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Renames `down_apply_pure_elim` to `down_pure_intro` and relocates it under the `# Pure` section of `DerivedLaws.lean`, matching #13582 as merged. Reverts the six `Invariant.withEarlyReturn`/`withEarlyReturnNewDo` variants to `abbrev` and reverts `Std/Data/String/ToNat.lean` to its pre-PR state, matching the final form of #13583. Updates the local `VCGen.lean` reference to the renamed `SPred.down_pure_intro` lemma and restores `mkFreshPair_triple` to legacy `mvcgen -elimLets +trivial` (it remains blocked under `mvcgen'`).
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This PR adds several entailment-related lemmas to
Std.Do.SPredandStd.Do.PostCond, intended for goal-decomposition during program verification proof automation.SPred.down_pure_nilandSPred.apply_pure_cons(existingrfllemmas) become@[simp, grind =]. Drops the now-redundantpure_consargument fromsimpinconjunction_apply.SPred.entails_nil_introandSPred.entails_nil_pure_intro: introduction forms forentailsatSPred [], mirroring the existingentails_cons_intro.SPred.down_pure_intro: derive(pure φ).downfromφ.SPred.apply_pure_cons_entails_l/_r: peel a state argument frompure (σ::σs) φ son either side of⊢ₛ.Std.Do.ExceptConds.entails.pure: closes any⊢ₑgoal atPostShape.pure, whereExceptConds.entailsreduces toTrue.