FKS2.floor_row1

theorem floor_row1 : ∀ x ∈ Set.Icc (Real.exp (4:ℝ)) (Real.exp (43:ℝ)),    Eπ x ≤ 2 * Real.log x * x ^ (-(1:ℝ) / 2) := by  have hcurve : ∀ y, Real.exp (4:ℝ) ≤ y →      Expr.eval (fun _ => Real.sqrt (Real.log y)) (xhalfCurveE 2 2)        ≤ 2 * Real.log y * y ^ (-(1:ℝ) / 2) := by    intro y hy    have hypos : (0:ℝ) < y := lt_of_lt_of_le (Real.exp_pos _) hy    have hyL : (0:ℝ) ≤ Real.log y := by      have h4 : (4:ℝ) ≤ Real.log y := by        rw [← Real.log_exp (4:ℝ)]; exact Real.log_le_log (Real.exp_pos _) hy      linarith    refine le_of_eq ?_    rw [eval_xhalfCurveE 2 2 y hypos hyL, Real.sq_sqrt hyL]    push_cast; ring  exact floor_xhalf_of_check (xhalfCurveE 2 2)    (fun x => 2 * Real.log x * x ^ (-(1:ℝ) / 2)) 4 2 93 (by norm_num)    (by rw [show ((2:ℚ):ℝ) = 2 by norm_num,          show (2:ℝ) = Real.sqrt (2 ^ 2) from (Real.sqrt_sq (by norm_num)).symm]        exact Real.sqrt_le_sqrt (by norm_num))    (by have h656 : Real.sqrt 43 ≤ 6.56 := by          rw [show (6.56:ℝ) = Real.sqrt (6.56 ^ 2) from (Real.sqrt_sq (by norm_num)).symm]          exact Real.sqrt_le_sqrt (by norm_num)        push_cast; linarith [h656])    (xhalfCurve_sub_supported 2 2) floor_slab_check_row1 hcurve