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Proof step 15 from proof unchNorec-validrefs-pathex (previous step)

¬ (validrefs(str, r1 ' + refs1 + r0 ', ty, st) ∧ ty ≤ mkclasstype(`java.lang.Object' .class)), 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) ⊦ validrefs(str, r1 ' + refs1 + r0 ', mkclasstype(`java.lang.Object' .class), st), 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 14:
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 ', mkclasstype(`java.lang.Object' .class), st), validrefs(str, r1 ' + refs1 + r0 ', ty, st0), validrefs(str, r1 ' + refs1 + r0 ', mkclasstype(`java.lang.Object' .class), st0), is_classtype(ty), is_arraytype(ty)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ mkclasstype (`java.lang.Object' .class) ↔ is_classtype(ty) ∨ is_arraytype(ty)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]