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Proof step 37 from proof unchNorec-validrefs-pathex (previous step)

refs = r1 + refs0, validrefs(str, refs, ty, st), r0 ∈ refs, ∀ r. r ∈ refs → unchangedNorec(r, st, st0) ⊦ refs = [], path∃(str, r1, r0, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
validrefs(str, r1 ' + refs0, ty, st), ∀ r. r = r1 ∨ r ∈ refs0 → unchangedNorec(r, st, st0) ⊦ path∃(str, r1, r0, st0), r0 ≠ r1 ∧ ¬ r0 ∈ refs0

Rule argument

[emptyarg]

Additional information

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