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Proof step 34 from proof unchNorec-validrefs-pathex (previous step)

validrefs(str, r1 ' + refs0, ty, st), r0 ∈ refs0, ∀ r. r = r1 ∨ r ∈ refs0 → unchangedNorec(r, st, st0) ⊦ r0 = r1, path∃(str, r1, r0, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ r ∈ refs ↔ (∃ refs0, refs1. refs = refs0 + (r + refs1))
Proof step 33:
validrefs(str, r1 ' + refs0, ty, st), ∃ refs2, refs1. refs0 = refs2 + (r0 + refs1), ∀ r. r = r1 ∨ r ∈ refs0 → unchangedNorec(r, st, st0) ⊦ r0 = r1, path∃(str, r1, r0, st0)

Rule argument

[x0lemmaarg: spec-name: list instance-name: references lemma-name: In antecedent: succedent: r ∈ refs ↔ (∃ refs0, refs1. refs = refs0 + (r + refs1)) substlist: [refs, r] → [refs0, r0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refs0, r0)]]