YaelDillies/APAP
Source indexedlemma · leanprover/lean4:v4.32.0
BohrSet.chordSet_subset_smul_arcSet
APAP.Prereqs.Bohr.Arc · APAP/Prereqs/Bohr/Arc.lean:48 to 60
Mathematical statement
Exact Lean statement
lemma chordSet_subset_smul_arcSet [Finite G] :
B.chordSet ⊆ ((π / 2) • B).arcSetComplete declaration
Lean source
Full Lean sourceLean 4
lemma chordSet_subset_smul_arcSet [Finite G] : B.chordSet ⊆ ((π / 2) • B).arcSet := fun x hx ψ => by rw [ewidth_smul] split case isFalse => simp case isTrue h => have := hx ψ simp only [←coe_width h, ENNReal.coe_le_coe, ←ENNReal.coe_mul, ←NNReal.coe_le_coe, coe_nnnorm, NNReal.coe_mul] at this ⊢ rw [coe_nnabs, abs_of_nonneg pi_div_two_pos.le, Real.norm_of_nonneg (angle_nonneg _ _), angle_comm] refine (Complex.angle_le_mul_norm_sub (by simp) (by simp)).trans ?_ gcongr