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Proof step 59 from proof junkrefs-put-nopathex-equiv (conclusion)

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

User applied rule structural induction

And obtained the following new goals

Proof step 58:
∀ 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))

Rule argument

[VARWITHVARSEQSARG : refs, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : references generated by [], +;])]]