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Proof step 58 from proof junkrefs-put-nopathex-equiv (previous step)

∀ str, r, r0, st, sk, ty, val. ¬ path∃(str, r, r0, st) ∧ is_valid_ref(str, r0, st) ∧ sk ≠ _type ∧ acc ≠ [] ∧ acc .first = r → (junkrefs(str, acc, ty, st[r0 -- sk, val]) ↔ junkrefs(str, acc, ty, st)) ⊦ ¬ path∃(str, r, r0, st) ∧ is_valid_ref(str, r0, st) ∧ sk ≠ _type ∧ r1 + acc ≠ [] ∧ (r1 + acc) .first = r → (junkrefs(str, r1 + acc, ty, st[r0 -- sk, val]) ↔ junkrefs(str, r1 + acc, ty, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
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)) ⊦ sk = _type, junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val]) ↔ junkrefs(str, r1 ' + acc, ty, st), path∃(str, r1, r0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]