Theorems · Definition · general topology
IsometryEquiv.subLeft
{G : Type v} →
[inst : AddGroup G] → [inst_1 : PseudoEMetricSpace G] → [IsIsometricVAdd G G] → [IsIsometricVAdd Gᵃᵒᵖ G] → G → G ≃ᵢ GSubtraction y ↦ x - y as an IsometryEquiv.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- AddGroupstatement and proof · cited by 4,410
- PseudoEMetricSpacestatement and proof · cited by 1,536
- AddOppositestatement and proof · cited by 452
- IsometryEquivstatement · cited by 177
- IsIsometricVAddstatement and proof · cited by 74
- Equiv.subLeftproof · cited by 10
- edist_sub_leftproof · cited by 0
Cited by4
Results whose statement or proof uses this declaration.
- QuotientAddGroup.norm_mkproof · cited by 2
- IsometryEquiv.subLeft_applystatement and proof · cited by 1
- IsometryEquiv.subLeft_symm_applystatement and proof · cited by 1
- IsometryEquiv.subLeft_toEquivstatement and proof · cited by 0