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Proof step 24 from proof prepost-wl-get-free-min (previous step)

¬ boolvar ↔ free-ecs(wlar, m0) = ∅, wlar[m0] = wl-entry(m, stat), m0 < # wlar, boolvar → n = free-ecs(wlar, m0).min ⊦ stat = free ∧ (¬ boolvar ∨ m < n), (boolvar → n = (stat = free ⊃ free-ecs(wlar, m0) ++ m;free-ecs(wlar, m0)).min) ∧ (¬ boolvar ↔ (stat = free ⊃ free-ecs(wlar, m0) ++ m;free-ecs(wlar, m0)) = ∅)

User applied rule case distinction

And obtained the following new goals

Proof step 25:
¬ boolvar ↔ free-ecs(wlar, m0) = ∅, wlar[m0] = wl-entry(m, stat), boolvar, m0 < # wlar, boolvar → n = free-ecs(wlar, m0).min ⊦ n = (stat = free ⊃ free-ecs(wlar, m0) ++ m;free-ecs(wlar, m0)).min, stat = free ∧ (¬ boolvar ∨ m < n)

Rule argument

pos: right 2

Additional information

Used simplifier rules: ⊦ ∅ ≠ ns ++ n; (s)