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Proof step 21 from proof validrefs-nodups (previous step)

refs2 .last = jvmref, r ∈ refs2, validrefs(str, r ' + refs2, ty, st), ∀ st, ty, str, refs0. # refs0 < # (r + refs2) → ( validrefs(str, refs0, ty, st) ∧ refs0 ≠ [] ∧ refs0 .last = jvmref → (∃ refs1. validrefs(str, refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref ∧ refs0 .first = refs1 .first ∧ ¬ dups(refs1) ∧ refs1 ⊆ refs0)) ⊦ refs2 = [], ∃ refs. validrefs(str, refs, ty, st) ∧ refs ≠ [] ∧ refs .last = jvmref ∧ r = refs .first ∧ ¬ dups(refs) ∧ refs ⊆ refs .first ' + refs2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ r ∈ refs ↔ (∃ refs0, refs1. refs = refs0 + (r + refs1))
Proof step 20:
refs2 .last = jvmref, ∃ refs0, refs1. refs2 = refs0 + (r + refs1), validrefs(str, r ' + refs2, ty, st), ∀ st, ty, str, refs0. # refs0 < # (r + refs2) → ( validrefs(str, refs0, ty, st) ∧ refs0 ≠ [] ∧ refs0 .last = jvmref → (∃ refs1. validrefs(str, refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref ∧ refs0 .first = refs1 .first ∧ ¬ dups(refs1) ∧ refs1 ⊆ refs0)) ⊦ refs2 = [], ∃ refs. validrefs(str, refs, ty, st) ∧ refs ≠ [] ∧ refs .last = jvmref ∧ r = refs .first ∧ ¬ dups(refs) ∧ refs ⊆ refs .first ' + refs2

Rule argument

[speclemmaarg: ,r ∈ refs ↔ (∃ refs0, refs1. refs = refs0 + (r + refs1)) ,[refs, r] → [refs2, r] ,F ,list ,references ,In ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refs2, r)]]