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Proof step 27 from proof cyclic-put-nopathex (previous step)

validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st), r0 ∈ refs1 ⊦ sk = _type, r0 = r1, r0 = r, validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st[r0 -- sk, val]), path∃(str, r, r0, st), junkref(str, r, st), dups(refs1), r ∈ refs1, r1 ≠ r ∧ ¬ r1 ∈ refs1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ ¬ path∃(str, r, r0, st) ∧ r0 ∈ refs → ¬ validrefs(str, r ' + refs, ty, st)

Rule argument

[crewrite-arg: validrefs-nopathex , F , [str, r, r0, st, refs, ty] → [str, r, r0, st, refs1 + r1 ', st[r -- _type] .type] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ refs → r ∈ refs + refs0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (str, r, r0, st, refs1 + r1 ', st[r -- _type] .type)]]