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Proof step 56 from proof junkrefs-put-nopathex-equiv (previous step)

junkrefs(str, r1 ' + acc, ty, st), is_valid_ref(str, r0, st), ∀ str0, r2, st0, sk0, ty0, val0. ¬ path∃(str0, acc .first, r2, st0) ∧ is_valid_ref(str0, r2, st0) ∧ sk0 ≠ _type ∧ acc ≠ [] → (junkrefs(str0, acc, ty0, st0[r2 -- sk0, val0]) ↔ junkrefs(str0, acc, ty0, st0)) ⊦ junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val]), sk = _type, path∃(str, r1, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → junkrefs(str, r ' + refs, ty, st)
Proof step 55:
¬ (r1 ≠ jvmref ∧ (¬ is_valid_ref(str, r1, st[r0 -- sk, val]) ∨ ¬ (st[r0 -- sk, val][r1 -- _type]) .type ≤ ty)), junkrefs(str, r1 ' + acc, ty, st), is_valid_ref(str, r0, st), ∀ str0, r2, st0, sk0, ty0, val0. ¬ path∃(str0, acc .first, r2, st0) ∧ is_valid_ref(str0, r2, st0) ∧ sk0 ≠ _type ∧ acc ≠ [] → (junkrefs(str0, acc, ty0, st0[r2 -- sk0, val0]) ↔ junkrefs(str0, acc, ty0, st0)) ⊦ junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val]), sk = _type, path∃(str, r1, 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, acc, r1, str] ,F ,junkrefs , ,junkrefs-is-junk ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- sk, val], ty, acc, r1, str)]]