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Proof step 12 from proof unchanged-pathex-append (previous step)

validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st), unchanged(str, r, st, st1), validrefs(str, (r ' + refs1) .last ' + refs0, mkclasstype(`java.lang.Object' .class), st), r1 = (r ' + refs1) .last ∨ r1 ∈ refs0 ⊦ unchangedNorec(r1, st, st1), path∃(str, (r ' + refs1) .last, ((r ' + refs1) .last ' + refs0) .last, st1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ unchanged(str, refs .first, st, st0) ∧ validrefs(str, refs, ty, st) ∧ r0 ∈ refs → unchangedNorec(r0, st, st0)
Proof step 11:
¬ ( unchanged(str, (r ' + refs1 + refs0) .first, st, st1) ∧ validrefs(str, r ' + refs1 + refs0, mkclasstype(`java.lang.Object' .class), st) ∧ r1 ∈ r ' + refs1 + refs0), validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st), unchanged(str, r, st, st1), validrefs(str, (r ' + refs1) .last ' + refs0, mkclasstype(`java.lang.Object' .class), st), r1 = (r ' + refs1) .last ∨ r1 ∈ refs0 ⊦ unchangedNorec(r1, st, st1), path∃(str, (r ' + refs1) .last, ((r ' + refs1) .last ' + refs0) .last, st1)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: unchanged-validrefs-unchNorec antecedent: succedent: unchanged(str, refs .first, st, st0) ∧ validrefs(str, refs, ty, st) ∧ r0 ∈ refs → unchangedNorec(r0, st, st0) substlist: [str, refs, st, st0, ty, r0] → [str, r ' + refs1 + refs0, st, st1, mkclasstype(`java.lang.Object' .class), r1] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, r ' + refs1 + refs0, st, st1, mkclasstype(`java.lang.Object' .class), r1)]]