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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 x

Complete declaration

Lean source

Canonical 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 : ) ^ 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]