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Proof step 54 from proof junkrefs-put-nopathex-equiv (previous step)

junkrefs(str, r1 ' + acc, ty, st), is_valid_ref(str, r0, st), is_valid_ref(str, r1, st[r0 -- sk, val]), st[r1 -- _type] .type ≤ ty, ∀ 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)) ⊦ sk = _type, r1 = jvmref, junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val]), path∃(str, r1, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ r ≠ r0 → (is_valid_ref(str, r0, st[r -- sk, val]) ↔ is_valid_ref(str, r0, st))
Proof step 5:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)
Proof step 53:
r0 ≠ r1, junkrefs(str, r1 ' + acc, ty, st), is_valid_ref(str, r0, st), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ 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)) ⊦ sk = _type, r1 = jvmref, junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val]), path∃(str, r1, r0, st)

Rule argument

[speclemmaarg: , r ≠ r0 → ( is_valid_ref(str, r0, st[r -- sk, val]) ↔ is_valid_ref(str, r0, st)) ,[val, sk, r, st, r0, str] → [val, sk, r0, st, r1, str] ,F ,addfuns , ,is_valid_ref-put-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (val, sk, r0, st, r1, str)]]