Theorems · Theorem · group theory
AddCon.induction_on
∀ {M : Type u_1} [inst : Add M] {c : AddCon M} {C : c.Quotient → Prop} (q : c.Quotient), (∀ (x : M), C ↑x) → C qThe inductive principle used to prove propositions about the elements of a quotient by an additive congruence relation.
- Defined in
- Mathlib.GroupTheory.Congruence.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddConstatement and proof · cited by 138
- Quotient.inductionOn'proof · cited by 69
- AddCon.Quotientstatement and proof · cited by 54
- AddCon.toQuotientstatement and proof · cited by 38
Cited by2
Results whose statement or proof uses this declaration.
- TensorProduct.induction_onproof · cited by 81
- PiTensorProduct.induction_on'proof · cited by 3