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Proof step 18 from proof prepost-wl-free-max-below (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ below(ns ++ n, m) = (n < m ⊃ below(ns -- n, m) ++ n;below(ns -- n, m))
Proof step 20:
¬ boolvar ↔ below(free-ecs(wlar, m3), n) = ∅, wlar[m3] = wl-entry(m2, free), wlar[m0] = wl-entry(m1, free), wlar[vtblpnum] = wl-entry(m, stat), m3 < # wlar, m0 < # wlar, m1 < n, m2 < n, boolvar → vtblpnum < # wlar, boolvar → vtblpnum < # wlar ∧ stat = free ∧ m = below(free-ecs(wlar, m3), n).max, ¬ boolvar ∨ m < m2 ⊦ m2 = (m2 < n ⊃ below(free-ecs(wlar, m3) -- m2, n) ++ m2;below(free-ecs(wlar, m3) -- m2, n)).max ∧ (m2 < n ⊃ below(free-ecs(wlar, m3) -- m2, n) ++ m2;below(free-ecs(wlar, m3) -- m2, n)) ≠ ∅

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, m2, free-ecs(wlar, m3)] flags: <all paths>

Additional information

Used terms: n, m2, free-ecs(wlar, m3)