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Proof step 27 from proof prepost-wl-get-used-min (previous step)

¬ boolvar ↔ used-ecs(wlar, m0) = ∅, wlar[m0] = wl-entry(m, stat), wlar[vtblpnum] = wl-entry(m1, stat0), boolvar, m0 < # wlar, stat = used → boolvar → vtblpnum < # wlar, boolvar → vtblpnum < m0 ∧ stat0 = used ∧ m1 = used-ecs(wlar, m0).min ⊦ (boolvar → ¬ m0 < vtblpnum ∧ stat0 = used ∧ m1 = (stat = used ⊃ used-ecs(wlar, m0) ++ m;used-ecs(wlar, m0)).min) ∧ (¬ boolvar ↔ (stat = used ⊃ used-ecs(wlar, m0) ++ m;used-ecs(wlar, m0)) = ∅), stat = used ∧ (¬ boolvar ∨ m < m1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
wlar[m0] = wl-entry(m, stat), wlar[vtblpnum] = wl-entry(used-ecs(wlar, m0).min, used), vtblpnum < # wlar, vtblpnum < m0, m0 < # wlar, vtblpnum + 1 < # wlar ⊦ # used-ecs(wlar, m0) = 0, used-ecs(wlar, m0) = ∅, used-ecs(wlar, m0).min = (stat = used ⊃ used-ecs(wlar, m0) ++ m;used-ecs(wlar, m0)).min ∧ (stat = used ⊃ used-ecs(wlar, m0) ++ m;used-ecs(wlar, m0)) ≠ ∅, stat = used ∧ m < used-ecs(wlar, m0).min

Rule argument

Additional information

Used simplifier rules: size-zero: ⊦ # ns ≠ 0 → ns ≠ ∅; (forward) from specification set-basic[nat-set]% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s)