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Proof step 125 from proof hasSharing-dd-help (previous step)

validrefs(str, (r ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st), validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), validrefs(str, (r ' + refs3) .last ' + refs2 + r0 ', st[(r ' + refs3) .last -- _type] .type, st), validrefs(str, r ' + refs3, st[r -- _type] .type, st) ⊦ r0 = jvmref, r1 = r0, (r ' + refs3) .last = r1, hasSharing(r, st), path∃(str, r1, (r ' + refs3) .last, st), path∃(str, (r ' + refs3) .last, r1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ refs ≠ [] → (r ' + refs) .last = refs .last
Proof step 124:
refs3 ≠ [], validrefs(str, (r ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st), validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), validrefs(str, refs3 .last ' + refs2 + r0 ', st[refs3 .last -- _type] .type, st), validrefs(str, r ' + refs3, st[r -- _type] .type, st) ⊦ r0 = jvmref, r1 = r0, refs3 .last = r1, hasSharing(r, st), path∃(str, r1, refs3 .last, st), path∃(str, refs3 .last, r1, st)

Rule argument

[speclemmaarg: ,refs ≠ [] → (r ' + refs) .last = refs .last ,[refs, r] → [refs3, r] ,F ,list-last ,references ,l-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' .last = r], [CSIMPSEQ : ⊦ ¬ path∃(str, r, r0, st) → ¬ validrefs (str, r ' + refs + r0 ', ty, st)])], [EXTRATERMS : (refs3, r)]]