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Proof step 208 from proof pathex-put-nopathex (previous step)

validrefs(str, r ' + refs0, st[r -- _type] .type, st), ∀ val, r0, sk, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st[r0 -- sk, val])) ⊦ sk = _type, path∃(str, r, (r ' + refs0) .last, st[r0 -- sk, val]), junkref(str, r, st), path∃(str, r, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 101:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 207:
¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ st[r -- _type] .type)), validrefs(str, r ' + refs0, st[r -- _type] .type, st), ∀ val, r0, sk, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st[r0 -- sk, val])) ⊦ sk = _type, path∃(str, r, (r ' + refs0) .last, st[r0 -- sk, val]), junkref(str, r, st), path∃(str, r, r0, st)

Rule argument

[crewrite-arg: validrefs-is-junk , F , [st, ty, refs, r, str] → [st, st[r -- _type] .type, refs0, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r -- _type] .type, refs0, r, str)]]