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Proof step 36 from proof prepost-wl-free-max-below (previous step)

wlar[m3] = wl-entry(m, free), wlar[m0] = wl-entry(m1, free), wlar[vtblpnum] = wl-entry(below(free-ecs(wlar, m3), n).max, free), vtblpnum < # wlar, m3 < # wlar, m0 < # wlar, m1 < n, m < n, m ≤ below(free-ecs(wlar, m3), n).max ⊦ # below(free-ecs(wlar, m3), n) = 0, below(free-ecs(wlar, m3), n).max = (below(free-ecs(wlar, m3), n) ++ m).max, below(free-ecs(wlar, m3), n) = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ (ns ++ n).max = (ns = ∅ ⊃ n;(n < ns.max ⊃ ns.max;n))
Proof step 38:
wlar[vtblpnum] = wl-entry(below(free-ecs(wlar, m3), n).max, free), wlar[m0] = wl-entry(m1, free), wlar[m3] = wl-entry(m, free), m < n, m1 < n, m0 < # wlar, m3 < # wlar, vtblpnum < # wlar, m ≤ below(free-ecs(wlar, m3), n).max ⊦ # below(free-ecs(wlar, m3), n) = 0, below(free-ecs(wlar, m3), n).max = (below(free-ecs(wlar, m3), n) = ∅ ⊃ m;(m < below(free-ecs(wlar, m3), n).max ⊃ below(free-ecs(wlar, m3), n).max;m)), below(free-ecs(wlar, m3), n) = ∅

Rule argument

spec: oset, inst: nat-set name: max-ifins seq: ⊦ (ns ++ n).max = (ns = ∅ ⊃ n;(n < ns.max ⊃ ns.max;n)) subst: [n, ns] → [m, below(free-ecs(wlar, m3), n)] flags: <all paths>

Additional information

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