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Proof step 16 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) ⊦ 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ validrefs(str, refs, ty, st) ∧ ty ≤ ty0 → validrefs(str, refs, ty0, st)
Proof step 15:
¬ (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)

Rule argument

[x0lemmaarg: spec-name: cyclic instance-name: lemma-name: validrefs-superclass antecedent: succedent: validrefs(str, refs, ty, st) ∧ ty ≤ ty0 → validrefs(str, refs, ty0, st) substlist: [str, refs, ty, st, ty0] → [str, r1 ' + refs1 + r0 ', ty, st, mkclasstype(`java.lang.Object' .class)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0)) dummy: () ]

Additional information

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