p : ℕ
inst✝ : Fact (Nat.Prime p)
F : Polynomial ℤ_[p]
a : ℤ_[p]
hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2
hnsol : Polynomial.eval a F ≠ 0
h : ‖Polynomial.eval a F‖ / ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2 < 1
⊢ T_gen p F a < 1
p : ℕ
inst✝ : Fact (Nat.Prime p)
F : Polynomial ℤ_[p]
a : ℤ_[p]
hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2
hnsol : Polynomial.eval a F ≠ 0
⊢ T_gen p F a < 1
have h := (div_lt_one (deriv_sq_norm_pos hnorm)).2 hnorm
p : ℕ
inst✝ : Fact (Nat.Prime p)
F : Polynomial ℤ_[p]
a : ℤ_[p]
hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2
hnsol : Polynomial.eval a F ≠ 0
h : ‖Polynomial.eval a F‖ / ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2 < 1
⊢ ‖Polynomial.eval a F‖ / ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2 < 1
p : ℕ
inst✝ : Fact (Nat.Prime p)
F : Polynomial ℤ_[p]
a : ℤ_[p]
hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2
hnsol : Polynomial.eval a F ≠ 0
h : ‖Polynomial.eval a F‖ / ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2 < 1
⊢ T_gen p F a < 1
rw [T_def]
no goals
p : ℕ
inst✝ : Fact (Nat.Prime p)
F : Polynomial ℤ_[p]
a : ℤ_[p]
hnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2
hnsol : Polynomial.eval a F ≠ 0
h : ‖Polynomial.eval a F‖ / ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2 < 1
⊢ ‖Polynomial.eval a F‖ / ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2 < 1
exact h