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theorem proved tactic proof

totalDeficit_flat

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formal statement (Lean)

 157theorem totalDeficit_flat {nH : ℕ}
 158    (hinges : Fin nH → SimplicialHingeData)
 159    (hFlat : ∀ h : Fin nH,
 160      DihedralAngle.FlatSumCondition (hinges h).dihedrals) :
 161    totalDeficit hinges = 0 := by

proof body

Tactic-mode proof.

 162  unfold totalDeficit
 163  apply Finset.sum_eq_zero
 164  intro h _
 165  have : (hinges h).deficit = 0 := by
 166    unfold SimplicialHingeData.deficit
 167    exact DihedralAngle.deficit_eq_zero_of_flat _ (hFlat h)
 168  rw [this]; ring
 169
 170/-! ## §6. Certificate -/
 171
 172/-- Phase C3 certificate. -/

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