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Proof step 15 from proof hasSharing-pathex (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(refs1 .first), hasSharing(refs1 .first, st), is_obj(str, r, st), hasSharing(r0, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, refs1 + r0 ', ty, st), ∀ st, r, str, refs. # refs < # (refs1 .first ' + refs1 .rest + r0 ') → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ r = jvmref, refs1 = [], hasSharing(r, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
refs1 = r1 + refs0, st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), hasSharing(r1, st), is_obj(str, r, st), hasSharing(r0, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, refs1 + r0 ', ty, st), ∀ st, r, str, refs. # refs < # (r1 ' + refs0 + r0 ') → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ r = jvmref, refs1 = [], hasSharing(r, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs1, r1, refs0] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs1, r1, refs0)]]