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Proof step 27 from proof validrefs-put-statfield (previous step)

st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str, ty, st, sk, val. validrefs(str, acc, ty, st[jvmref -- sk, val]) ↔ validrefs(str, acc, ty, st) ⊦ validrefs(str, r ' + acc, ty, st[jvmref -- sk, val]) ↔ acc = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)), r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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 26:
is_obj(str, r, st[jvmref -- sk, val]) ∧ (st[jvmref -- sk, val][r -- _type]) .type ≤ ty, st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str, ty, st, sk, val. validrefs(str, acc, ty, st[jvmref -- sk, val]) ↔ validrefs(str, acc, ty, st) ⊦ acc = [] ∨ (∃ fs. fs ' ∈ instfields((st[jvmref -- sk, val][r -- _type]) .type .class) ∧ is_referencevalue(st[jvmref -- sk, val][r -- fs ']) ∧ acc .first = (st[jvmref -- sk, val][r -- fs ']) .refval ∧ validrefs(str, acc, fs .type, st[jvmref -- sk, val])) ↔ acc = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)), r = jvmref

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st[jvmref -- sk, val], ty, acc, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_obj (str, r, st[jvmref -- sk, val]) ↔ is_obj(str, r, st)], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]])], [EXTRATERMS : (st[jvmref -- sk, val], ty, acc, r, str)]]