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Proof step 28 from proof prepost-wl-get-used-min (previous step)

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

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 29:
wlar[vtblpnum] = wl-entry(used-ecs(wlar, m0).min, used), wlar[m0] = wl-entry(m, stat), vtblpnum + 1 < # wlar, m0 < # wlar, vtblpnum < m0, vtblpnum < # wlar ⊦ # used-ecs(wlar, m0) = 0, used-ecs(wlar, m0).min = (stat = used ⊃ used-ecs(wlar, m0) ++ m;used-ecs(wlar, m0)).min, used-ecs(wlar, m0) = ∅, stat = used ∧ m < used-ecs(wlar, m0).min, 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)) ≠ ∅

Rule argument

fma: used-ecs(wlar, m0).min = (stat = used ⊃ used-ecs(wlar, m0) ++ m;used-ecs(wlar, m0)).min

Additional information

Used simplifier rules: ⊦ ∅ ≠ ns ++ n; (s) Used formulas: used-ecs(wlar, m0).min = (stat = used ⊃ used-ecs(wlar, m0) ++ m;used-ecs(wlar, m0)).min