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Proof step 17 from proof hasSharing-pathex (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
refs ≠ [] ⊦ refs + refs0 = r ' + refs1 ↔ r = refs .first ∧ refs1 = refs .rest + refs0
Proof step 16:
refs1 ≠ [], r1 = refs1 .first ∧ refs0 = refs1 .rest + r0 ', st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), is_obj(str, r, st), hasSharing(r0, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r1 ' + refs0, ty, st), r0 ∈ refs0, r1 ∈ refs1, hasSharing(r1, st), ∀ st, r, str, refs. # refs < # (r1 ' + refs0) → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ refs0 = [], r = jvmref, hasSharing(r, st)

Rule argument

[speclemmaarg: refs ≠ [] , refs + refs0 = r ' + refs1 ↔ r = refs .first ∧ refs1 = refs .rest + refs0 ,[refs1, r, refs0, refs] → [refs0, r1, r0 ', refs1] ,F ,list ,references-olista ,firsteq-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ [] + refs = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' = r0 ' + refs ↔ r = r0 ∧ refs = []])], [EXTRATERMS : (refs0, r1, r0 ', refs1)]]