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Proof step 7 from proof unchanged-cyclic (previous step)

unchanged(str, r, st, st0), validrefs(str, r ' + refs1, st[r -- _type] .type, st) ⊦ validrefs(str, r ' + refs1, st0[r -- _type] .type, st0), junkref(str, r, st), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ (∀ r. r ∈ refs → unchangedNorec(r, st, st0)) → (validrefs(str, refs, ty, st) ↔ validrefs(str, refs, ty, st0))
Proof step 6:
¬ (∀ r0. r0 ∈ r ' + refs1 → unchangedNorec(r0, st, st0)), unchanged(str, r, st, st0), validrefs(str, r ' + refs1, st[r -- _type] .type, st) ⊦ validrefs(str, r ' + refs1, st0[r -- _type] .type, st0), junkref(str, r, st), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: unchNorec-validrefs-equiv antecedent: succedent: (∀ r. r ∈ refs → unchangedNorec(r, st, st0)) → ( validrefs(str, refs, ty, st) ↔ validrefs(str, refs, ty, st0)) substlist: [st0, st, ty, refs, str] → [st0, st, st[r -- _type] .type, r ' + refs1, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : cyclic, , validrefs-sametype, ⊦ ¬ validrefs (str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs (str, r ' + refs, ty, st)])], [EXTRATERMS : (st0, st, st[r -- _type] .type, r ' + refs1, str)]]