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Proof step 67 from proof junkrefs-put-nopathex (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val]), ∀ str0, r2, st0, ty0, sk0, val0. ¬ path∃(str0, acc .first, r2, st0) ∧ ¬ junkrefs(str0, acc, ty0, st0) ∧ sk0 ≠ _type ∧ acc ≠ [] → ¬ junkrefs(str0, acc, ty0, st0[r2 -- sk0, val0]) ⊦ sk = _type, 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])]]