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Proof step 6 from proof ecs-n-write (previous step)

n0 < # wlar, ∀ wlar, m, wle. n0 ≤ # wlar → ecs(wlar[m, wle], n0) = (m < n0 ⊃ (ecs(wlar, n0) -- wlar[m].ec) ++ wle.ec;ecs(wlar, n0)) ⊦ ecs(wlar[m, wle], n0 + 1) = (wlar[n0].ec = wlar[m].ec ⊃ ecs(wlar, n0);(ecs(wlar, n0) -- wlar[m].ec) ++ wlar[n0].ec) ++ wle.ec, n0 < m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
n0 < # wlar, m < # wlar, m ≤ n0, ∀ wlar, m, wle. n0 ≤ # wlar → ecs(wlar[m, wle], n0) = (m < n0 ⊃ (ecs(wlar, n0) -- wlar[m].ec) ++ wle.ec;ecs(wlar, n0)) ⊦ ecs(wlar[m, wle], n0 + 1) = (wlar[n0].ec = wlar[m].ec ⊃ ecs(wlar, n0);(ecs(wlar, n0) -- wlar[m].ec) ++ wlar[n0].ec) ++ wle.ec

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)