Mathlib Map

Theorems · Theorem · geometry

AffineMap.lineMap_apply_one

∀ {k : Type u_1} {V1 : Type u_2} {P1 : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V1] [inst_2 : Module k V1]
  [inst_3 : AddTorsor V1 P1] (p₀ p₁ : P1), (AffineMap.lineMap p₀ p₁) 1 = p₁
Defined in
Mathlib.LinearAlgebra.AffineSpace.AffineMap
Cited by
37 results in Mathlib
Foundations
Depth 45 from the axioms · uses propext, Quot.sound
Assumes
RingAddCommGroupModuleAddTorsor

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le · cited by 9Convex.norm_image_sub_le_…dist_lineMap_right · cited by 7dist_lineMap_rightSbtw.angle₁₂₃_eq_pi · cited by 6Sbtw.angle₁₂₃_eq_piWbtw.wOppSide₁₃ · cited by 4Wbtw.wOppSide₁₃Manifold.riemannianEDist_le_pathELength · cited by 4Manifold.riemannianEDist_…Sbtw.mem_image_Ioo · cited by 3Sbtw.mem_image_Ioodist_sq_lineMap_of_inner_eq_zero · cited by 3dist_sq_lineMap_of_inner_…Wbtw.trans_expand_left · cited by 2Wbtw.trans_expand_leftComplex.norm_eqOn_closedBall_of_isMaxOn · cited by 2Complex.norm_eqOn_closedB…List.exists_map_eq_of_sorted_nonempty_iff_wbtw · cited by 2List.exists_map_eq_of_sor…lineMap_le_right_iff_le · cited by 2lineMap_le_right_iff_leAffine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint · cited by 2ExcenterExists.sign_signe…Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint · cited by 2ExcenterExists.sign_signe…IsMinOn.of_isLocalMinOn_of_convexOn · cited by 2IsMinOn.of_isLocalMinOn_o…dist_sq_of_inner_eq_zero · cited by 2dist_sq_of_inner_eq_zeroDFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupRing · cited by 7463RingHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddTorsor · cited by 1657AddTorsorone_smul · cited by 1374one_smulVSub.vsub · cited by 817VSub.vsubAffineMap · cited by 674AffineMapAffineMap.lineMap · cited by 254AffineMap.lineMapvsub_vadd · cited by 62vsub_vaddAffineMap.lineMap_apply_oneCITED BYCITES

Cites11

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Cited by37

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