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Proof step 6 from proof cyclic-subset-01 (previous step)

r -- _type ∈ st, st ⊆ st0, validrefs(str, r ' + refs0, st[r -- _type] .type, st), r ∈ st ⊦ validrefs(str, r ' + refs0, st[r -- _type] .type, st0), junkref(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ validrefs(str, refs, ty, st) ∧ st ⊆ st0 ∧ ¬ junkref(str, r, st) ∧ refs ≠ [] ∧ refs .first = r → validrefs(str, refs, ty, st0)

Rule argument

[crewrite-arg: validrefs-subset-01 , F , [str, refs, ty, st, st0, r] → [str, r ' + refs0, st[r -- _type] .type, st, st0, (r ' + refs0) .first] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []])], [EXTRATERMS : (str, r ' + refs0, st[r -- _type] .type, st, st0, (r ' + refs0) .first)]]