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Proof step 118 from proof junkrefs-put-nopathexplus-equiv (previous step)

junkrefs(str, r ' + refs0, ty, st), ∀ val, sk, r0, st, ty, r, str, refs. # refs < # refs0 → (junkrefs(str, r ' + refs, ty, st) → junkrefs(str, r ' + refs, ty, st[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r, r0, st)) ⊦ r = r0, r = jvmref, sk = _type, junkrefs(str, r ' + refs0, ty, st[r0 -- sk, val]), path∃+(str, r, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → junkrefs(str, r ' + refs, ty, st)
Proof step 117:
¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st[r0 -- sk, val]) ∨ ¬ (st[r0 -- sk, val][r -- _type]) .type ≤ ty)), junkrefs(str, r ' + refs0, ty, st), ∀ val, sk, r0, st, ty, r, str, refs. # refs < # refs0 → (junkrefs(str, r ' + refs, ty, st) → junkrefs(str, r ' + refs, ty, st[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r, r0, st)) ⊦ r = r0, r = jvmref, sk = _type, junkrefs(str, r ' + refs0, ty, st[r0 -- sk, val]), path∃+(str, r, r0, st)

Rule argument

[speclemmaarg: , r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → junkrefs(str, r ' + refs, ty, st) ,[st, ty, refs, r, str] → [st[r0 -- sk, val], ty, refs0, r, str] ,F ,junkrefs , ,junkrefs-is-junk ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- sk, val], ty, refs0, r, str)]]