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Proof step 33 from proof unchNorec-validrefs-pathex (previous step)

validrefs(str, r1 ' + refs0, ty, st), ∃ refs2, refs1. refs0 = refs2 + (r0 + refs1), ∀ r. r = r1 ∨ r ∈ refs0 → unchangedNorec(r, st, st0) ⊦ r0 = r1, path∃(str, r1, r0, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
validrefs(str, r1 ' + refs1 + r0 ' + refs, ty, st), ∀ r. r = r1 ∨ r ∈ refs1 ∨ r = r0 ∨ r ∈ refs → unchangedNorec(r, st, st0) ⊦ r0 = r1, path∃(str, r1, r0, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]