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Proof step 5 from proof pathex-put-last (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ¬ validrefs(str, refs + r0 ', ty, st) ∧ ¬ junkref(str, refs .first, st) ∧ refs ≠ [] ∧ ¬ r0 ∈ refs ∧ sk ≠ _type → ¬ validrefs(str, refs + r0 ', ty, st[r0 -- sk, val])

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (val, sk, st, st[r -- _type] .type, r0, r ' + refs1, str)]]