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Proof step 32 from proof weakmon-lem (previous step)

ii(m) < ii(m1), ii(m) < m0, m0 ≤ ii(m1), ∀ n. ii(n) ≤ ii(n + 1), ∀ n0, ii. n0 < m0 + 1 → (∀ n. ii(n) ≤ ii(n + 1)) → (∃ m. n0 ≤ ii(m)) ∨ (∃ n. (∀ m. ii(m) ≤ n) ∧ (∃ m. ii(m) = n)) ⊦ m0 = 0, ii(m) = m0, ii(m1) = 0, ∃ m. ii(m) = m0, ∃ m1. m0 < ii(m1), ∃ n. (∀ m. ii(m) ≤ n) ∧ (∃ m. ii(m) = n)

User applied rule exists right

And obtained the following new goals

Proof step 33:
ii(m) < ii(m1), ii(m) < m0, m0 ≤ ii(m1), ∀ n. ii(n) ≤ ii(n + 1), ∀ n0, ii. n0 < m0 + 1 → (∀ n. ii(n) ≤ ii(n + 1)) → (∃ m. n0 ≤ ii(m)) ∨ (∃ n. (∀ m. ii(m) ≤ n) ∧ (∃ m. ii(m) = n)) ⊦ m0 = 0, ii(m) = m0, ii(m1) = 0, ∃ m. ii(m) = m0, m0 < ii(m1), ∃ m1. m0 < ii(m1), ∃ n. (∀ m. ii(m) ≤ n) ∧ (∃ m. ii(m) = n)

Rule argument

pos: right 5 terms: m1 abort: F discard: F computed: F

Additional information

Used terms: m1