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Proof step 6 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 ⊦ validrefs(str, r ' + refs1 + refs0, mkclasstype(`java.lang.Object' .class), st), unchangedNorec(r1, st, st1), path∃(str, (r ' + refs1) .last, ((r ' + refs1) .last ' + refs0) .last, st1)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 5:
⊦ validrefs(str, refs, ty, st) ∧ validrefs(str, refs0, ty0, st) ∧ refs .last = refs0 .first ∧ refs ≠ [] ∧ refs0 ≠ [] → validrefs(str, refs + refs0 .rest, ty, st)

Rule argument

[x0lemmaarg: spec-name: cyclic instance-name: lemma-name: validrefs-append-01 antecedent: succedent: validrefs(str, refs, ty, st) ∧ validrefs(str, refs0, ty0, st) ∧ refs .last = refs0 .first ∧ refs ≠ [] ∧ refs0 ≠ [] → validrefs(str, refs + refs0 .rest, ty, st) substlist: [str, refs, ty, st, refs0, ty0] → [str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st, (r ' + refs1) .last ' + refs0, mkclasstype(`java.lang.Object' .class)] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (r ' + refs) .rest = refs])], [EXTRATERMS : (str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st, (r ' + refs1) .last ' + refs0, mkclasstype(`java.lang.Object' .class))]]