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Proof step 3 from proof ecs-n-write (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 4:
n0 +1 ≤ # 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) = (m < n0 +1 ⊃ (ecs(wlar, n0 +1) -- wlar[m].ec) ++ wle.ec;ecs(wlar, n0 +1))

Rule argument

indvar: n

Additional information

Used simplifier rules: ecs-n-base: ⊦ ecs(wlar, 0) = ∅;%nat freely generated by 0, +1;;% ⊦ ¬ m < 0; (s)