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Proof step 8 from proof disjoint-def-pathex (previous step)

path∃(str, r0, r, st), path∃(str, r1, r, st), r0 ∈ refs, r1 ∈ refs, ∀ refs0, refs1. refs0 = [] ∨ refs1 = [] ∨ ¬ refs0 .first ∈ refs ∨ ¬ refs1 .first ∈ refs ∨ refs0 .first = refs1 .first ∨ refs0 .last ≠ refs1 .last ∨ refs0 .last = jvmref ∨ ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∨ ¬ validrefs(str, refs1, st[refs1 .first -- _type] .type, st) ⊦ r = jvmref, r1 = r0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 7:
∃ refs. refs ≠ [] ∧ refs .first = r0 ∧ refs .last = r ∧ validrefs(str, refs, st[r0 -- _type] .type, st), path∃(str, r1, r, st), r0 ∈ refs, r1 ∈ refs, ∀ refs0, refs1. refs0 = [] ∨ refs1 = [] ∨ ¬ refs0 .first ∈ refs ∨ ¬ refs1 .first ∈ refs ∨ refs0 .first = refs1 .first ∨ refs0 .last ≠ refs1 .last ∨ refs0 .last = jvmref ∨ ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∨ ¬ validrefs(str, refs1, st[refs1 .first -- _type] .type, st) ⊦ r = jvmref, r1 = r0

Rule argument

[x0lemmaarg: spec-name: cyclic instance-name: lemma-name: pathex-def-simple antecedent: succedent: path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, st[r -- _type] .type, st)) substlist: [st, r0, r, str] → [st, r, r0, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, r0, str)]]