feat: deleteEdges-straddling = induce sumCompl disjoint sum — #2965#2979
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Add induce_sum_map_sumCompl_eq_deleteEdges (SumGraph.lean): for a predicate p,
deleting every edge whose endpoints lie on different sides of p decomposes G
into the disjoint sum of the two induced subgraphs, up to Equiv.sumCompl p:
((G.induce {p}) ⊕g (G.induce {¬p})).map (Equiv.sumCompl p)
= G.deleteEdges {e | e straddles p}
Proved by edge extensionality (4-case analysis on Sum constructors): an edge
survives iff its endpoints are adjacent and on the same side of p. This is the
structural identity behind component factorization of a bond-deleted (cut)
finite-volume system — Step 2 of the exhaustion-increment bridge.
Part of #2965
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This was referenced May 26, 2026
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* feat: straddle-set no-cross + not-internal facts (Part of #2965) * feat: straddle-set no-cross + not-internal facts Add two graph-level facts about the straddle (cut) edge set of induce_sum_map_sumCompl_eq_deleteEdges: - straddle_not_mem_of_same_side: p a ↔ p b ⇒ s(a,b) ∉ straddle (the deleted set contains no same-side edge), feeding inducedGraph_deleteEdges_eq_of_not_internal. - deleteEdges_straddle_no_cross: p a, ¬p b ⇒ ¬(G.deleteEdges {straddle}).Adj a b (the bond-deleted graph disconnects the two sides), the no-cross hypothesis for correlation_inducedGraph_union_inl_of_no_cross applied to G.deleteEdges {straddle}. Pure adjacency facts (no Fintype), bridging #2979/#2981/#2978 toward the bond-deletion → isolated-component capstone via the working inducedGraph route. Part of #2965 Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.7 <noreply@anthropic.com>
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Part of #2965
Adds the Step 2 structural core (in
SumGraph.lean):induce_sum_map_sumCompl_eq_deleteEdges: for a predicatep, deleting every edge whose endpoints lie on different sides ofpdecomposesGinto the disjoint sum of the two induced subgraphs, up toEquiv.sumCompl p:((G.induce {p}) ⊕g (G.induce {¬p})).map (Equiv.sumCompl p) = G.deleteEdges {e | e straddles p}.Proved by edge extensionality (4-case analysis on
Sumconstructors): an edge survives the deletion iff its endpoints are adjacent and on the same side ofp. This is the structural identity behind component factorization of a bond-deleted (cut) finite-volume system — Step 2 of the exhaustion-increment bridge (after #2975–#2978 give the correlation-level factorization machinery).lake build IsingModel.SumGraphgreen, sorry 0, file linter-clean, tex compiles.🤖 Generated with Claude Code