AffineSubspace.map_bot
∀ {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_3} {V₂ : Type u_4} {P₂ : Type u_5} [inst : Ring k]
[inst_1 : AddCommGroup V₁] [inst_2 : Module k V₁] [inst_3 : AddTorsor V₁ P₁] [inst_4 : AddCommGroup V₂]
[inst_5 : Module k V₂] [inst_6 : AddTorsor V₂ P₂] (f : P₁ →ᵃ[k] P₂), AffineSubspace.map f ⊥ = ⊥- Cited by
- 7 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- Bot.botstatement and proof · cited by 4,720
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement · cited by 871
- AffineMapstatement and proof · cited by 674
- AffineSubspace.mapstatement and proof · cited by 78
- Set.image_emptyproof · cited by 73
- AffineSubspace.coe_injectiveproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- AffineSubspace.map_spanproof · cited by 16
- AffineSubspace.shift_botproof · cited by 2
- AffineSubspace.direction_shiftproof · cited by 1
- AffineSubspace.map_eq_bot_iffproof · cited by 1
- AffineSubspace.shift_eq_map_homothetyproof · cited by 0
- AffineSubspace.pointwise_vadd_botproof · cited by 0
- AffineSubspace.smul_botproof · cited by 0