feat: generalize induce-univ correlation to any full set — #2965#2985
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Add correlation_induce_of_forall_mem: if s contains every vertex (∀ x, x ∈ s), then correlation (G.induce s) p A = correlation G p (A.map (subtypeUnivEquiv hs)), since G.induce s ≃g G. Generalizes correlation_induce_univ from Set.univ to any full set. Applies to s = ↑(S ∪ Sᶜ) (full by Finset.union_compl), letting the Phase A capstone's inducedGraph _ (S ∪ Sᶜ) left side connect to the raw bond-deleted graph WITHOUT forcing the propositional Finset equality S ∪ Sᶜ = univ at the type level — the clean route through the per-stage-increment type-transport. Part of #2965 Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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Part of #2965 (per-stage increment type-transport).
Adds
correlation_induce_of_forall_mem(InducedUnion.lean): if∀ x, x ∈ sthencorrelation (G.induce s) p A = correlation G p (A.map (Equiv.subtypeUnivEquiv hs))— sinceG.induce s ≃g G. Generalizescorrelation_induce_univ(#2984) fromSet.univto any full set.The point: applying it with
s = ↑(S ∪ Sᶜ)(full byFinset.union_compl) lets the capstone'sinducedGraph _ (S ∪ Sᶜ)left side (#2983) connect to the raw bond-deleted graph without forcing the propositional Finset equalityS ∪ Sᶜ = univat the type level — the clean route through the per-stage-increment type-transport flagged in #2965.lake build IsingModel.AmbientLatticeSum.InducedUniongreen, sorry 0, file linter-clean, tex compiles.🤖 Generated with Claude Code