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Proof step 26 from proof validrefs-put-notin-02 (previous step)

acc + r0 ' = st[r1 -- mkfs(class0, ty1, fieldvar0) '] .refval ' + refs, st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st), okval(val, ty0), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class0, ty1, fieldvar0) ']), validrefs(str, acc + r0 ', ty1, st), ∀ str, r0, ty, st, val, ty0, class, fieldvar, r. validrefs(str, acc + r0 ', ty, st) ∧ okval(val, ty0) → mkfs(class, ty0, fieldvar) ' = _length ∨ mkfs(class, ty0, fieldvar) ' = _type ∨ validrefs(str, acc + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∨ r ∈ acc ⊦ r1 = jvmref, r = r1, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, r ∈ acc, ∃ fs0. fs0 ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs0 ']) ∧ (acc + r0 ') .first = st[r1 -- fs0 '] .refval ∧ validrefs(str, acc + r0 ', fs0 .type, st[r -- mkfs(class, ty0, fieldvar) ', val]), r0 ≠ st[r1 -- mkfs(class0, ty1, fieldvar0) '] .refval ∧ ¬ r0 ∈ refs, ¬ st[r1 -- mkfs(class0, ty1, fieldvar0) '] .refval ∈ acc ∧ st[r1 -- mkfs(class0, ty1, fieldvar0) '] .refval ≠ r0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 25:
acc + r0 ' = r2 + refs0 ∧ acc + r0 ' ≠ [], acc + r0 ' = st[r1 -- mkfs(class0, ty1, fieldvar0) '] .refval ' + refs, st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st), okval(val, ty0), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class0, ty1, fieldvar0) ']), validrefs(str, acc + r0 ', ty1, st), ∀ str, r0, ty, st, val, ty0, class, fieldvar, r. validrefs(str, acc + r0 ', ty, st) ∧ okval(val, ty0) → mkfs(class, ty0, fieldvar) ' = _length ∨ mkfs(class, ty0, fieldvar) ' = _type ∨ validrefs(str, acc + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∨ r ∈ acc ⊦ r1 = jvmref, r = r1, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, r ∈ acc, ∃ fs0. fs0 ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs0 ']) ∧ r2 = st[r1 -- fs0 '] .refval ∧ validrefs(str, acc + r0 ', fs0 .type, st[r -- mkfs(class, ty0, fieldvar) ', val]), r0 ≠ st[r1 -- mkfs(class0, ty1, fieldvar0) '] .refval ∧ ¬ r0 ∈ refs, ¬ st[r1 -- mkfs(class0, ty1, fieldvar0) '] .refval ∈ acc ∧ st[r1 -- mkfs(class0, ty1, fieldvar0) '] .refval ≠ r0

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [acc + r0 ', r2, refs0] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (acc + r0 ', r2, refs0)]]