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Proof step 8 from proof pathex-levelsubset-01 (previous step)

level⊆(str, str0), validref(str, r, ty, st), validrefs(str0, r ' + refs0, st[r -- _type] .type, st) ⊦ refs0 = [], r = refs0 .last, dups(refs0), r ∈ refs0, validrefs(str, r ' + refs0, st[r -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validrefs-levelsubset-01 antecedent: succedent: level⊆(str, str0) ∧ validrefs(str0, refs, ty0, st) ∧ validref(str, refs .first, ty, st) → validrefs(str, refs, ty0, st) substlist: [ty, str0, st, ty0, refs, str] → [ty, str0, st, st[r -- _type] .type, r ' + refs0, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 4)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, c-08, ⊦ (r ' + refs) .first = r], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (ty, str0, st, st[r -- _type] .type, r ' + refs0, str)]]