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Proof step 8 from proof weakmon-lem (previous step)

m0 ≤ m, ∀ n. ii(n) ≤ ii(n + 1), ∀ m. ii(m) ≤ ii(m0) ⊦ ii(m) = ii(m0)

User applied rule structural induction

And obtained the following new goals

Proof step 9:
m0 ≤ m1 +1, ∀ m. ii(m) ≤ ii(m0), ∀ n. ii(n) ≤ ii(n + 1), ∀ m0, ii. m0 ≤ m1 ∧ (∀ n. ii(n) ≤ ii(n + 1)) ∧ (∀ m. ii(m) ≤ ii(m0)) → ii(m1) = ii(m0) ⊦ ii(m1 +1) = ii(m0)

Rule argument

indvar: m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ m ≤ 0 ↔ m = 0; (s)