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Proof step 13 from proof validrefs-put-array-badindex (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r2), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- mkfs(class, ty1, fieldvar) ']), validrefs(str, r2 ' + refs, ty1, st[r -- i ', val]), i < 0, is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, r2 ' + refs, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = jvmref, ∃ fs0. fs0 ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs0 ']) ∧ r2 = st[r0 -- fs0 '] .refval ∧ validrefs(str, st[r0 -- fs0 '] .refval ' + refs, fs0 .type, st)

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-13 antecedent: succedent: is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) substlist: [val, r] → [st[r0 -- mkfs(class, ty1, fieldvar) '], r2] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r0 -- mkfs(class, ty1, fieldvar) '], r2)]]