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Proof step 30 from proof prepost-wl-get-used-min (previous step)

wlar[m0] = wl-entry(m, used), wlar[vtblpnum] = wl-entry(used-ecs(wlar, m0).min, used), vtblpnum < # wlar, vtblpnum < m0, m0 < # wlar, vtblpnum + 1 < # wlar, used-ecs(wlar, m0).min ≤ m ⊦ # used-ecs(wlar, m0) = 0, used-ecs(wlar, m0).min = (used-ecs(wlar, m0) ++ m).min, used-ecs(wlar, m0) = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ n ∈ ns ∧ ¬ n0 < n → (ns ++ n0).min = ns.min

Rule argument

spec: oset, inst: nat-set name: min-ins-01 seq: ⊦ n ∈ ns ∧ ¬ n0 < n → (ns ++ n0).min = ns.min subst: [n, n0, ns] → [used-ecs(wlar, m0).min, m, used-ecs(wlar, m0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ ns.min ∈ ns ↔ ns ≠ ∅; (ss) Used terms: used-ecs(wlar, m0).min, m, used-ecs(wlar, m0)