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Proof step 4 from proof ecs-write (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ n ≤ # wlar → ecs(wlar[m, wle], n) = (m < n ⊃ (ecs(wlar, n) -- wlar[m].ec) ++ wle.ec;ecs(wlar, n))
Proof step 6:
# wlar ≤ # wlar ⊦ (m < # wlar ⊃ (ecs(wlar, # wlar) -- wlar[m].ec) ++ wle.ec;ecs(wlar, # wlar)) = (m < # wlar ⊃ (ecs(wlar) -- wlar[m].ec) ++ wle.ec;ecs(wlar))

Rule argument

spec: <toplevel> name: ecs-n-write seq: ⊦ n ≤ # wlar → ecs(wlar[m, wle], n) = (m < n ⊃ (ecs(wlar, n) -- wlar[m].ec) ++ wle.ec ;ecs(wlar, n) ) subst: [n, wle, m, wlar] → [# wlar, wle, m, wlar] flags: <all paths>

Additional information

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