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Proof step 30 from proof unchNorec-validrefs-pathex (previous step)

validrefs(str, r1 ' + refs1 + r0 ' + refs, ty, st), ∀ r. r = r1 ∨ r ∈ refs1 ∨ r = r0 ∨ r ∈ refs → unchangedNorec(r, st, st0) ⊦ r0 = r1, r1 ' + refs1 + r0 ' ≠ [] ∧ (r1 ' + refs1 + r0 ') .first = r1 ∧ (r1 ' + refs1 + r0 ') .last = r0 ∧ validrefs(str, r1 ' + refs1 + r0 ', mkclasstype(`java.lang.Object' .class), st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
validrefs(str, r1 ' + refs1 + r0 ' + refs, ty, st), ∀ r. r = r1 ∨ r ∈ refs1 ∨ r = r0 ∨ r ∈ refs → unchangedNorec(r, st, st0) ⊦ r0 = r1, validrefs(str, r1 ' + refs1 + r0 ', mkclasstype(`java.lang.Object' .class), st0)

Rule argument

[emptyarg]

Additional information

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