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Proof step 26 from proof disjoint-def-pathex (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 25:
refs1 = r2 + refs2, refs1 .last = refs0 .last, r2 ∈ refs, refs0 .first ∈ refs, validrefs(str, refs1, st[r2 -- _type] .type, st), validrefs(str, refs0, st[refs0 .first -- _type] .type, st), ∀ r, r0, r1. ¬ r ∈ refs ∨ ¬ r0 ∈ refs ∨ r = r0 ∨ r1 = jvmref ∨ ¬ path∃(str, r, r1, st) ∨ ¬ path∃(str, r0, r1, st) ⊦ refs1 = [], refs0 = [], r2 = refs0 .first, refs0 .last = jvmref

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: references lemma-name: elim-1 antecedent: succedent: refs ≠ [] → (r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0) substlist: [refs, r, refs0] → [refs1, r2, refs2] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ refs ≠ [] → ( r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0)])], [EXTRATERMS : (refs1, r2, refs2)]]