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Proof step 11 from proof cyclic-put-nopathex (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ¬ path∃(str, r, r0, st) ∧ r0 ∈ refs → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 10:
¬ (¬ path∃(str, r, r0, st[r0 -- sk, val]) ∧ r0 ∈ refs1 + r1 '), validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st[r0 -- sk, val]) ⊦ sk = _type, r0 = r, validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st), path∃(str, r, r0, st), junkref(str, r, st), dups(refs1), r ∈ refs1, r1 ≠ r ∧ ¬ r1 ∈ refs1, r0 ≠ r1 ∧ ¬ r0 ∈ refs1

Rule argument

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

Additional information

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