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Proof step 46 from proof validrefs-nodups (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
refs2 .last = jvmref, validrefs(str, r ' + refs2, ty, st), dups(refs2), ∀ 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 = [], r ∈ refs2, ∃ refs. validrefs(str, refs, ty, st) ∧ refs ≠ [] ∧ refs .last = jvmref ∧ r = refs .first ∧ ¬ dups(refs) ∧ refs ⊆ refs .first ' + refs2

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]