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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).arcSet

Complete declaration

Lean source

Canonical 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