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Proof step 52 from proof validrefs-put-notin-01 (previous step)

acc + r0 ' = st[r1 -- i '] .refval ' + refs, 0 < st[r1 -- _length] .intval, 0 ≤ i, st[r1 -- _type] .type ≤ ty, okval(val, ty1), r -- mkfs(class, ty1, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty1, fieldvar) '], ty1), r ∈ st, is_array(str, r1, st), validrefs(str, acc + r0 ', st[r1 -- _type] .type .type, st[r -- mkfs(class, ty1, fieldvar) ', val]), is_referencevalue(st[r1 -- i ']), i < st[r1 -- _length] .intval, ∀ r2, fs0, val0, st0, str0, r3, ty0. ¬ r2 ∈ acc ∧ fs0 ' ≠ _type ∧ fs0 ' ≠ _length ∧ okval(val0, fs0 .type) ∧ r2 -- fs0 ' ∈ st0 ∧ okval(st0[r2 -- fs0 '], fs0 .type) → (validrefs(str0, acc + r3 ', ty0, st0[r2 -- fs0 ', val0]) ↔ validrefs(str0, acc + r3 ', ty0, st0)) ⊦ r = r1, r1 = jvmref, mkfs(class, ty1, fieldvar) ' = _length, mkfs(class, ty1, fieldvar) ' = _type, r ∈ acc, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ st[r1 -- i '] .refval = st[r1 -- i0 '] .refval ∧ validrefs(str, st[r1 -- i0 '] .refval ' + refs, st[r1 -- _type] .type .type, st), r0 ≠ st[r1 -- i '] .refval ∧ ¬ r0 ∈ refs, ¬ st[r1 -- i '] .refval ∈ acc ∧ st[r1 -- i '] .refval ≠ r0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r1 -- i '], r4] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r1 -- i '], r4)]]