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Proof step 41 from proof prepost-wl-free-max-below (previous step)

¬ boolvar ↔ below(free-ecs(wlar, m3), n) = ∅, wlar[vtblpnum] = wl-entry(m2, stat0), wlar[m0] = wl-entry(m1, free), wlar[m3] = wl-entry(m, free), m1 < n, m0 < # wlar, m3 < # wlar, m < n → boolvar → vtblpnum < # wlar, boolvar → vtblpnum < # wlar ∧ stat0 = free ∧ m2 = below(free-ecs(wlar, m3), n).max ⊦ ¬ boolvar ↔ below(free-ecs(wlar, m3) ++ m, n) = ∅, m < n ∧ (¬ boolvar ∨ m2 < m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ below(ns ++ n, m) = (n < m ⊃ below(ns -- n, m) ++ n;below(ns -- n, m))

Rule argument

spec: wlarray name: below-rec seq: ⊦ below(ns ++ n, m) = (n < m ⊃ below(ns -- n, m) ++ n;below(ns -- n, m)) subst: [m, n, ns] → [n, m, free-ecs(wlar, m3)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m > n ↔ n < m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n > m ⊦ below(ns -- m, n) = below(ns, n) -- m; (s)% ⊦ (ns -- n) ++ n = ns ++ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%n ≤ m ⊦ below(ns -- m, n) = below(ns, n); (s)% ⊦ ∅ ≠ ns ++ n; (s) Used terms: n, m, free-ecs(wlar, m3)