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Proof step 47 from proof validrefs-put-notin-02 (previous step)

(acc + r0 ') .first = st[r1 -- i '] .refval, is_array(str, r1, st), okval(val, ty0), st[r1 -- _type] .type ≤ ty, i < st[r1 -- _length] .intval, is_referencevalue(st[r1 -- i ']), validrefs(str, acc + r0 ', st[r1 -- _type] .type .type, st), 0 ≤ i, 0 < st[r1 -- _length] .intval, ∀ 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, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 46:
acc + r0 ' = r2 + refs ∧ acc + r0 ' ≠ [], r2 = st[r1 -- i '] .refval, is_array(str, r1, st), okval(val, ty0), st[r1 -- _type] .type ≤ ty, i < st[r1 -- _length] .intval, is_referencevalue(st[r1 -- i ']), validrefs(str, acc + r0 ', st[r1 -- _type] .type .type, st), 0 ≤ i, 0 < st[r1 -- _length] .intval, ∀ 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, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val])

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [acc + r0 ', r2, refs] ,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, refs)]]