DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

doc: More doc strings.

Browse source
This commit is contained in:
jstoobysmith 2024-11-12 06:33:58 +00:00
parent c24029c9ca
commit c6fdcbbe7d
3 changed files with 14 additions and 0 deletions
Download patch file Download diff file Expand all files Collapse all files

6
HepLean/FlavorPhysics/CKMMatrix/StandardParameterization/StandardParameters.lean
View file

@ -70,14 +70,17 @@ def δ₁₃ (V : Quotient CKMMatrixSetoid) : ℝ :=
section sines
/-- For a CKM matrix `sin θ₁₂` is non-negative. -/
lemma S₁₂_nonneg (V : Quotient CKMMatrixSetoid) : 0 ≤ S₁₂ V := by
rw [S₁₂, div_nonneg_iff]
apply Or.inl
apply (And.intro (VAbs_ge_zero 0 1 V) (Real.sqrt_nonneg (VudAbs V ^ 2 + VusAbs V ^ 2)))
/-- For a CKM matrix `sin θ₁₃` is non-negative. -/
lemma S₁₃_nonneg (V : Quotient CKMMatrixSetoid) : 0 ≤ S₁₃ V :=
VAbs_ge_zero 0 2 V
/-- For a CKM matrix `sin θ₂₃` is non-negative. -/
lemma S₂₃_nonneg (V : Quotient CKMMatrixSetoid) : 0 ≤ S₂₃ V := by
by_cases ha : VubAbs V = 1
· rw [S₂₃, if_pos ha]
@ -86,6 +89,7 @@ lemma S₂₃_nonneg (V : Quotient CKMMatrixSetoid) : 0 ≤ S₂₃ V := by
apply Or.inl
apply And.intro (VAbs_ge_zero 1 2 V) (Real.sqrt_nonneg (VudAbs V ^ 2 + VusAbs V ^ 2))
/-- For a CKM matrix `sin θ₁₂` is less then or equal to 1. -/
lemma S₁₂_leq_one (V : Quotient CKMMatrixSetoid) : S₁₂ V ≤ 1 := by
rw [S₁₂, @div_le_one_iff]
by_cases h1 : √(VudAbs V ^ 2 + VusAbs V ^ 2) = 0
@ -101,9 +105,11 @@ lemma S₁₂_leq_one (V : Quotient CKMMatrixSetoid) : S₁₂ V ≤ 1 := by
simp only [Fin.isValue, le_add_iff_nonneg_left]
exact sq_nonneg (VAbs 0 0 V)
/-- For a CKM matrix `sin θ₁₃` is less then or equal to 1. -/
lemma S₁₃_leq_one (V : Quotient CKMMatrixSetoid) : S₁₃ V ≤ 1 :=
VAbs_leq_one 0 2 V
/-- For a CKM matrix `sin θ₂₃` is less then or equal to 1. -/
lemma S₂₃_leq_one (V : Quotient CKMMatrixSetoid) : S₂₃ V ≤ 1 := by
by_cases ha : VubAbs V = 1
· rw [S₂₃, if_pos ha]