Theorems · Theorem · ring theory
TrivSqZeroExt.ind
∀ {R : Type u_3} {M : Type u_4} [inst : AddZeroClass R] [inst_1 : AddZeroClass M] {P : TrivSqZeroExt R M → Prop},
(∀ (r : R) (m : M), P (TrivSqZeroExt.inl r + TrivSqZeroExt.inr m)) → ∀ (x : TrivSqZeroExt R M), P xTo show a property hold on all TrivSqZeroExt R M it suffices to show it holds
on terms of the form inl r + inr m.
- Defined in
- Mathlib.Algebra.TrivSqZeroExt.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- AddZeroClassAddZeroClass
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddZeroClassstatement and proof · cited by 1,237
- TrivSqZeroExtstatement and proof · cited by 180
- TrivSqZeroExt.inlstatement and proof · cited by 64
- TrivSqZeroExt.inrstatement and proof · cited by 59
- TrivSqZeroExt.inl_fst_add_inr_snd_eqproof · cited by 5
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