Mathlib Map

Theorems · Theorem · geometry

AffineMap.lineMap_apply_zero

∀ {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) 0 = p₀
Defined in
Mathlib.LinearAlgebra.AffineSpace.AffineMap
Cited by
40 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_left · cited by 7dist_lineMap_leftSbtw.angle₁₂₃_eq_pi · cited by 6Sbtw.angle₁₂₃_eq_piWbtw.angle₂₁₃_eq_zero_of_ne · cited by 5Wbtw.angle₂₁₃_eq_zero_of_…Wbtw.wOppSide₁₃ · cited by 4Wbtw.wOppSide₁₃wbtw_iff_left_eq_or_right_mem_image_Ici · cited by 4wbtw_iff_left_eq_or_right…Manifold.riemannianEDist_le_pathELength · cited by 4Manifold.riemannianEDist_…Sbtw.mem_image_Ioo · cited by 3Sbtw.mem_image_Ioowbtw_smul_vadd_smul_vadd_of_nonneg_of_le · cited by 3wbtw_smul_vadd_smul_vadd_…Complex.norm_eqOn_closedBall_of_isMaxOn · cited by 2Complex.norm_eqOn_closedB…Complex.norm_le_of_forall_mem_frontier_norm_le · cited by 2Complex.norm_le_of_forall…List.exists_map_eq_of_sorted_nonempty_iff_wbtw · cited by 2List.exists_map_eq_of_sor…Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint · cited by 2ExcenterExists.sign_signe…wbtw_swap_left_iff · cited by 2wbtw_swap_left_iffIsMinOn.of_isLocalMinOn_of_convexOn · cited by 2IsMinOn.of_isLocalMinOn_o…DFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupRing · cited by 7463RingHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddTorsor · cited by 1657AddTorsorVSub.vsub · cited by 817VSub.vsubzero_smul · cited by 716zero_smulAffineMap · cited by 674AffineMapAffineMap.lineMap · cited by 254AffineMap.lineMapzero_vadd · cited by 95zero_vaddAffineMap.lineMap_apply_zeroCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by40

Results whose statement or proof uses this declaration.