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Proof step 21 from proof unchNorec-validrefs-pathex (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ validrefs(str, refs, ty, st) ∧ (∀ r. r ∈ refs → unchangedNorec(r, st, st0)) → validrefs(str, refs, ty, st0)
Proof step 20:
¬ (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)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: unchNorec-validrefs antecedent: succedent: validrefs(str, refs, ty, st) ∧ (∀ r. r ∈ refs → unchangedNorec(r, st, st0)) → validrefs(str, refs, ty, st0) substlist: [st, st0, ty, refs, str] → [st, st0, mkclasstype(`java.lang.Object' .class), r1 ' + refs1 + r0 ', str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, st0, mkclasstype(`java.lang.Object' .class), r1 ' + refs1 + r0 ', str)]]