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Proof step 55 from proof junkrefs-put-nopathex-equiv (previous step)

¬ (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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ junkrefs (str, jvmref ' + refs, ty, st)], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]