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Proof step 55 from proof prepost-wl-free-max-below (previous step)

wlar[vtblpnum] = wl-entry(m, stat), wlar[m0] = wl-entry(m1, free), m0 < # wlar, m1 < n ⊦ m1 ∈ free-ecs(wlar, # wlar), vtblpnum < # wlar ∧ stat = free ∧ m = ∅.max

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
m0 ≤ # wlar ⊦ n ∈ free-ecs(wlar, m0) ↔ (∃ m. m < m0 ∧ wlar[m].status = free ∧ wlar[m].ec = n)
Proof step 57:
wlar[m0] = wl-entry(m1, free), wlar[vtblpnum] = wl-entry(m, stat), m1 < n, m0 < # wlar, # wlar ≤ # wlar ⊦ ∃ m. m < # wlar ∧ wlar[m].status = free ∧ wlar[m].ec = m1, vtblpnum < # wlar ∧ stat = free ∧ m = ∅.max

Rule argument

spec: wlarray name: in-free-h seq: m0 ≤ # wlar ⊦ n ∈ free-ecs(wlar, m0) ↔ (∃ m. m < m0 ∧ wlar[m].status = free ∧ wlar[m].ec = n) subst: [m0, wlar, n] → [# wlar, wlar, m1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ n < n; (s) Used terms: # wlar, wlar, m1