AffineMap.lineMap_apply_module
∀ {k : Type u_1} {V1 : Type u_2} [inst : Ring k] [inst_1 : AddCommGroup V1] [inst_2 : Module k V1] (p₀ p₁ : V1) (c : k),
(AffineMap.lineMap p₀ p₁) c = (1 - c) • p₀ + c • p₁- Cited by
- 16 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- one_smulproof · cited by 1,374
- AffineMapstatement · cited by 674
- AffineMap.lineMapstatement · cited by 254
- smul_subproof · cited by 142
- sub_smulproof · cited by 97
Cited by16
Results whose statement or proof uses this declaration.
- segment_eq_image_lineMapproof · cited by 11
- openSegment_eq_image_lineMapproof · cited by 6
- AffineMap.contDiff_lineMap_uncurryproof · cited by 5
- lineMap_mono_leftproof · cited by 2
- lineMap_le_lineMap_iff_of_ltproof · cited by 2
- lineMap_lt_lineMap_iff_of_ltproof · cited by 2
- AffineMap.lineMap_apply_ringproof · cited by 2
- lineMap_mono_rightproof · cited by 1
- lineMap_slope_slope_sub_div_subproof · cited by 1
- lineMap_strict_mono_rightproof · cited by 1
- Finset.lineMap_affineCombinationproof · cited by 1
- IsVisible.of_convexHull_of_posproof · cited by 1