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Proof step 29 from proof cyclic-put-nopathex (previous step)

validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st) ⊦ validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st[r0 -- sk, val]), sk = _type, 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 22:
⊦ ¬ r ∈ refs → (validrefs(str, refs, ty, st[r -- sk, val]) ↔ validrefs(str, refs, ty, st))
Proof step 28:
¬ ¬ r0 ∈ (r ' + refs1) + r1 ', validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st) ⊦ validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st[r0 -- sk, val]), sk = _type, path∃(str, r, r0, st), junkref(str, r, st), dups(refs1), r ∈ refs1, r1 ≠ r ∧ ¬ r1 ∈ refs1

Rule argument

[crewrite-arg: validrefs-put-notin , F , [val, sk, r, st, ty, refs, str] → [val, sk, r0, st, st[r -- _type] .type, (r ' + refs1) + r1 ', str] ]

Additional information

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