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Proof step 136 from proof hasSharing-dd-help (previous step)

path∃(str, r, r2, st), validrefs(str, (r ' + refs0) .last ' + refs1 + r0 ', st[(r ' + refs0) .last -- _type] .type, st), validrefs(str, r2 ' + refs2 + r0 ', st[r2 -- _type] .type, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ (r ' + refs0) .last = r0, r0 = jvmref, r2 = (r ' + refs0) .last, hasSharing(r, st), path∃(str, r2, (r ' + refs0) .last, st), path∃(str, (r ' + refs0) .last, r2, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ refs ≠ [] → (r ' + refs) .last = refs .last
Proof step 135:
refs0 ≠ [], path∃(str, r, r2, st), validrefs(str, refs0 .last ' + refs1 + r0 ', st[refs0 .last -- _type] .type, st), validrefs(str, r2 ' + refs2 + r0 ', st[r2 -- _type] .type, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ refs0 .last = r0, r0 = jvmref, r2 = refs0 .last, hasSharing(r, st), path∃(str, r2, refs0 .last, st), path∃(str, refs0 .last, r2, st)

Rule argument

[speclemmaarg: ,refs ≠ [] → (r ' + refs) .last = refs .last ,[refs, r] → [refs0, r] ,F ,list-last ,references ,l-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' .last = r])], [EXTRATERMS : (refs0, r)]]