 157
 158/-! ## §4. Certificate -/
 159
 160structure DihedralAngleCert where
 161  cube_is_right_angle : cube_dihedral.theta = Real.pi / 2
 162  regular_tet_in_range :
 163    0 < regular_tet_dihedral.theta ∧ regular_tet_dihedral.theta < Real.pi
 164  cubic_flat_sum :
 165    FlatSumCondition [cube_dihedral, cube_dihedral, cube_dihedral, cube_dihedral]
 166  cubic_deficit_zero :
 167    deficit [cube_dihedral, cube_dihedral, cube_dihedral, cube_dihedral] = 0
 168  theta_in_range : ∀ d : DihedralAngleData, 0 ≤ d.theta ∧ d.theta ≤ Real.pi
 169  cos_theta_eq : ∀ d : DihedralAngleData, Real.cos d.theta = d.cosine
 170
 171theorem dihedralAngleCert : DihedralAngleCert where
 172  cube_is_right_angle := cube_dihedral_theta
 173  regular_tet_in_range := regular_tet_dihedral_in_open_interval
 174  cubic_flat_sum := cubic_lattice_flatSum
 175  cubic_deficit_zero := cubic_lattice_deficit_zero
 176  theta_in_range := fun d => ⟨theta_nonneg d, theta_le_pi d⟩
 177  cos_theta_eq := cos_theta
 178
 179end
 180
 181end DihedralAngle
 182end Geometry
 183end IndisputableMonolith

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.