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Proof step 20 from proof unchNorec-validrefs-pathex (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
validrefs(str, r1 ' + refs1 + r0 ' + refs, ty, st), validrefs(str, r1 ' + refs1 + r0 ', ty, st), ∀ r. r = r1 ∨ r ∈ refs1 ∨ r = r0 ∨ r ∈ refs → unchangedNorec(r, st, st0) ⊦ r0 = r1, validrefs(str, r1 ' + refs1 + r0 ', ty, st0), validrefs(str, r1 ' + refs1 + r0 ', mkclasstype(`java.lang.Object' .class), st0), validrefs(str, r1 ' + refs1 + r0 ', mkclasstype(`java.lang.Object' .class), st) ∧ (r = r1 ∨ r ∈ refs1 ∨ r = r0 → unchangedNorec(r, st, st0))

Rule argument

[emptyarg]

Additional information

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