a b c : Ordinal
b0 : b ≠ 0
h : IsLimit c
⊢ ¬a < b ^ c ↔ ∀ (x : Ordinal), ¬(x < c ∧ a < b ^ x)
a b c : Ordinal
b0 : b ≠ 0
h : IsLimit c
⊢ a < b ^ c ↔ ∃ c', c' < c ∧ a < b ^ c'
rw [← not_iff_not, not_exists]
no goals
a b c : Ordinal
b0 : b ≠ 0
h : IsLimit c
⊢ ¬a < b ^ c ↔ ∀ (x : Ordinal), ¬(x < c ∧ a < b ^ x)
simp only [not_lt, opow_le_of_limit b0 h, exists_prop, not_and]