fpvandoorn/carleson
Source indexedlemma · leanprover/lean4:v4.32.0
TileStructure.Forest.P7_5_4_le_adjointBoundaryOperator_mul
Carleson.ForestOperator.LargeSeparation · Carleson/ForestOperator/LargeSeparation.lean:1525 to 1535
Mathematical statement
Exact Lean statement
lemma P7_5_4_le_adjointBoundaryOperator_mul (mx : x ∈ ball (c J) (8⁻¹ * D ^ s J)) :
P7_5_4 t u₁ u₂ f₁ f₂ J ≤
adjointBoundaryOperator t u₁ f₁ x * adjointBoundaryOperator t u₂ f₂ xComplete declaration
Lean source
Full Lean sourceLean 4
lemma P7_5_4_le_adjointBoundaryOperator_mul (mx : x ∈ ball (c J) (8⁻¹ * D ^ s J)) : P7_5_4 t u₁ u₂ f₁ f₂ J ≤ adjointBoundaryOperator t u₁ f₁ x * adjointBoundaryOperator t u₂ f₂ x := by have mx' : x ∈ J := by refine ((ball_subset_ball ?_).trans ball_subset_Grid) mx change _ ≤ (D : ℝ) ^ s J / 4; rw [div_eq_inv_mul]; gcongr; norm_num unfold P7_5_4 adjointBoundaryOperator conv_lhs => enter [1]; rw [← add_zero (_ + _)] conv_lhs => enter [2]; rw [← add_zero (_ + _)] gcongr exacts [biInf_le _ mx, biInf_le _ mx', zero_le, biInf_le _ mx, biInf_le _ mx', zero_le]