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Proof step 73 from proof validrefs-put-last (previous step)

∀ str, r0, ty, st, sk, val. ¬ validrefs(str, acc + r0 ', ty, st) ∧ ¬ junkref(str, acc .first, st) ∧ acc ≠ [] ∧ ¬ r0 ∈ acc ∧ sk ≠ _type → ¬ validrefs(str, acc + r0 ', ty, st[r0 -- sk, val]) ⊦ ¬ validrefs(str, (r + acc) + r0 ', ty, st) ∧ ¬ junkref(str, (r + acc) .first, st) ∧ r + acc ≠ [] ∧ ¬ r0 ∈ r + acc ∧ sk ≠ _type → ¬ validrefs(str, (r + acc) + r0 ', ty, st[r0 -- sk, val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 72:
validrefs(str, (r ' + acc) + r0 ', ty, st[r0 -- sk, val]), ∀ str, r0, ty, st, sk, val. ¬ validrefs(str, acc + r0 ', ty, st) ∧ ¬ junkref(str, acc .first, st) ∧ acc ≠ [] ∧ ¬ r0 ∈ acc ∧ sk ≠ _type → ¬ validrefs(str, acc + r0 ', ty, st[r0 -- sk, val]) ⊦ sk = _type, r0 = r, r0 ∈ acc, junkref(str, r, st), validrefs(str, (r ' + acc) + r0 ', ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]