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Proof step 72 from proof validrefs-put-last (previous step)

validrefs(str, (r ' + acc) + r0 ', ty, st[r0 -- sk, val]), ∀ str, r0, ty, st, sk, val. ¬ validrefs(str, acc + r0 ', ty, st) ∧ ¬ junkref(str, acc .first, st) ∧ acc ≠ [] ∧ ¬ r0 ∈ acc ∧ sk ≠ _type → ¬ validrefs(str, acc + r0 ', ty, st[r0 -- sk, val]) ⊦ sk = _type, r0 = r, r0 ∈ acc, junkref(str, r, st), validrefs(str, (r ' + acc) + r0 ', ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 71:
¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st[r0 -- sk, val]) ∨ ¬ (st[r0 -- sk, val][r -- _type]) .type ≤ ty)), validrefs(str, (r ' + acc) + r0 ', ty, st[r0 -- sk, val]), ∀ str, r0, ty, st, sk, val. ¬ validrefs(str, acc + r0 ', ty, st) ∧ ¬ junkref(str, acc .first, st) ∧ acc ≠ [] ∧ ¬ r0 ∈ acc ∧ sk ≠ _type → ¬ validrefs(str, acc + r0 ', ty, st[r0 -- sk, val]) ⊦ sk = _type, r0 = r, r0 ∈ acc, junkref(str, r, st), validrefs(str, (r ' + acc) + r0 ', ty, st)

Rule argument

[crewrite-arg: validrefs-is-junk , F , [st, ty, refs, r, str] → [st[r0 -- sk, val], ty, acc + r0 ', r, str] ]

Additional information

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