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Proof step 30 from proof validrefs-put-notin-02 (previous step)

acc + r0 ' = st[r1 -- fs '] .refval ' + refs, validrefs(str, acc + r0 ', fs .type, st), is_referencevalue(st[r1 -- fs ']), fs ' ∈ instfields(st[r1 -- _type] .type .class), st[r1 -- _type] .type ≤ ty, okval(val, ty0), is_obj(str, r1, 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 ⊦ mkfs(class, ty0, fieldvar) ' = _length, mkfs(class, ty0, fieldvar) ' = _type, r = r1, r1 = jvmref, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]), r ∈ acc, r0 ≠ st[r1 -- fs '] .refval ∧ ¬ r0 ∈ refs, ¬ st[r1 -- fs '] .refval ∈ acc ∧ st[r1 -- fs '] .refval ≠ r0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 29:
is_obj(str, r1, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∧ (st[r -- mkfs(class, ty0, fieldvar) ', val][r1 -- _type]) .type ≤ ty, acc + r0 ' = st[r1 -- fs '] .refval ' + refs, validrefs(str, acc + r0 ', fs .type, st), is_referencevalue(st[r1 -- fs ']), fs ' ∈ instfields(st[r1 -- _type] .type .class), st[r1 -- _type] .type ≤ ty, okval(val, ty0), is_obj(str, r1, 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 ⊦ mkfs(class, ty0, fieldvar) ' = _length, mkfs(class, ty0, fieldvar) ' = _type, r = r1, r1 = jvmref, acc + r0 ' = [] ∨ (∃ fs. fs ' ∈ instfields((st[r -- mkfs(class, ty0, fieldvar) ', val][r1 -- _type]) .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ', val][r1 -- fs ']) ∧ (acc + r0 ') .first = (st[r -- mkfs(class, ty0, fieldvar) ', val][r1 -- fs ']) .refval ∧ validrefs(str, acc + r0 ', fs .type, st[r -- mkfs(class, ty0, fieldvar) ', val])), r ∈ acc, r0 ≠ st[r1 -- fs '] .refval ∧ ¬ r0 ∈ refs, ¬ st[r1 -- fs '] .refval ∈ acc ∧ st[r1 -- fs '] .refval ≠ r0

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st[r -- mkfs(class, ty0, fieldvar) ', val], ty, acc + r0 ', r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_obj (str, r0, st[r -- sk, val]) ↔ is_obj(str, r0, st))], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st[r -- mkfs(class, ty0, fieldvar) ', val], ty, acc + r0 ', r1, str)]]