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Proof step 5 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) = (¬ n0 < m ⊃ (wlar[n0].ec = wlar[m].ec ⊃ ecs(wlar, n0);(ecs(wlar, n0) -- wlar[m].ec) ++ wlar[n0].ec) ++ wle.ec;ecs(wlar, n0) ++ wlar[n0].ec)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 6:
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
Proof step 37:
n0 < # wlar, n0 < m, ∀ 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) = ecs(wlar, n0) ++ wlar[n0].ec

Rule argument

pos: right 1

Proof step 5 from proof ecs-n-write (previous step)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Rule argument

Additional information