Theorems · Theorem · ring theory
TrivSqZeroExt.isUnit_iff_isUnit_fst
∀ {R : Type u} {M : Type v} [inst : AddCommGroup M] [inst_1 : Semiring R] [inst_2 : Module Rᵐᵒᵖ M] [inst_3 : Module R M]
[inst_4 : SMulCommClass R Rᵐᵒᵖ M] {x : TrivSqZeroExt R M}, IsUnit x ↔ IsUnit x.fstWhen lowered to a prop, Matrix.invertibleEquivInvertibleFst forms an iff.
- Defined in
- Mathlib.Algebra.TrivSqZeroExt.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, 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.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- SMulCommClassstatement and proof · cited by 1,927
- IsUnitstatement · cited by 1,602
- MulOppositestatement and proof · cited by 1,135
- Invertibleproof · cited by 549
- TrivSqZeroExtstatement and proof · cited by 180
- TrivSqZeroExt.fststatement and proof · cited by 96
- Equiv.nonempty_congrproof · cited by 47
- TrivSqZeroExt.invertibleEquivInvertibleFstproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotentproof · cited by 0
- TrivSqZeroExt.isUnit_inl_iffproof · cited by 0