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Proof step 59 from proof hasSharing-pathex (previous step)

hasSharing(refs0 .last, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st), ∀ st, r, str, refs. # refs < # refs0 → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ refs0 = [], hasSharing(r, st)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 58:
refs0 = refs1 + r0 ', hasSharing(r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st), ∀ st, r, str, refs. # refs < # refs0 → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ refs0 = [], hasSharing(r, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r ' ,[refs, r, refs0] → [refs0, r0, refs1] ,T ,list-last ,references-olista ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r '])], [EXTRATERMS : (refs0, r0, refs1)]]