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Proof step 61 from proof validrefs-put-notin (previous step)

∀ str, ty, st, r, sk, val. (validrefs(str, acc, ty, st[r -- sk, val]) ↔ validrefs(str, acc, ty, st)) ∨ r ∈ acc ⊦ validrefs(str, r0 ' + acc, ty, st[r -- sk, val]) ↔ validrefs(str, r0 ' + acc, ty, st), r = r0, r ∈ acc

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ r = jvmref → (validrefs(str, r ' + refs, ty, st) ↔ refs = [])
Proof step 58:
r0 ≠ jvmref, ∀ str, ty, st, r, sk, val. (validrefs(str, acc, ty, st[r -- sk, val]) ↔ validrefs(str, acc, ty, st)) ∨ r ∈ acc ⊦ validrefs(str, r0 ' + acc, ty, st[r -- sk, val]) ↔ validrefs(str, r0 ' + acc, ty, st), r = r0, r ∈ acc
Proof step 59:
⊦ validrefs(str, jvmref ', ty, st)
Proof step 60:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []

Rule argument

[crewrite-arg: validrefs-null , F , [st, ty, refs, r, str] → [st[r -- sk, val], ty, acc, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st[r -- sk, val], ty, acc, r0, str)]]