Theorems · Theorem · ring theory
TrivSqZeroExt.inl_fst_add_inr_snd_eq
∀ {R : Type u} {M : Type v} [inst : AddZeroClass R] [inst_1 : AddZeroClass M] (x : TrivSqZeroExt R M),
TrivSqZeroExt.inl x.fst + TrivSqZeroExt.inr x.snd = x- Defined in
- Mathlib.Algebra.TrivSqZeroExt.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- AddZeroClassAddZeroClass
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.
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- AddZeroClassstatement and proof · cited by 1,237
- TrivSqZeroExtstatement and proof · cited by 180
- TrivSqZeroExt.fststatement · cited by 96
- TrivSqZeroExt.sndstatement · cited by 83
- TrivSqZeroExt.inlstatement · cited by 64
- TrivSqZeroExt.inrstatement · cited by 59
- TrivSqZeroExt.extproof · cited by 29
Cited by5
Results whose statement or proof uses this declaration.
- TrivSqZeroExt.hasSum_expSeries_of_smul_commproof · cited by 1
- TrivSqZeroExt.eq_smul_exp_of_invertibleproof · cited by 1
- TrivSqZeroExt.range_inlAlgHom_sup_adjoin_range_inrproof · cited by 0
- TrivSqZeroExt.indproof · cited by 0
- DualNumber.range_inlAlgHom_sup_adjoin_epsproof · cited by 0