AffineMap.lineMap_apply_one_sub
∀ {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) (c : k), (AffineMap.lineMap p₀ p₁) (1 - c) = (AffineMap.lineMap p₁ p₀) c- Cited by
- 8 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- mul_oneproof · cited by 3,885
- HVAdd.hVAddproof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- AffineMapstatement and proof · cited by 674
- mul_negproof · cited by 590
- DFunLikeproof · cited by 576
- sub_add_cancelproof · cited by 344
- zero_subproof · cited by 335
Cited by8
Results whose statement or proof uses this declaration.
- midpoint_commproof · cited by 14
- affineSegment_commproof · cited by 2
- map_le_lineMap_iff_slope_le_slope_rightproof · cited by 2
- openSegment_subset_unionproof · cited by 1
- AffineMap.lineMap_lineMap_leftproof · cited by 1
- AffineMap.right_vsub_lineMapproof · cited by 1
- Path.segment_symmproof · cited by 0
- AffineMap.lineMap_vsub_rightproof · cited by 0