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Theorems · Theorem · group theory

MulActionWithZero.nontrivial

∀ (M₀ : Type u_2) (A : Type u_7) [inst : MonoidWithZero M₀] [inst_1 : Zero A] [MulActionWithZero M₀ A] [Nontrivial A],
  Nontrivial M₀
Defined in
Mathlib.Algebra.GroupWithZero.Action.Defs
Cited by
3 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MonoidWithZeroZeroMulActionWithZeroNontrivial
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Module.nontrivial · cited by 17Module.nontrivialAlgebraic.infinite_of_charZero · cited by 1Algebraic.infinite_of_cha…IsFractionRing.isAlgebraic_iff' · cited by 0IsFractionRing.isAlgebrai…Nontrivial · cited by 2416NontrivialMonoidWithZero · cited by 456MonoidWithZerosubsingleton_or_nontrivial · cited by 161subsingleton_or_nontrivialMulActionWithZero · cited by 79MulActionWithZeronot_subsingleton · cited by 24not_subsingletonMulActionWithZero.subsingleton · cited by 3MulActionWithZero.subsing…MulActionWithZero.nontrivialCITED BYCITES

Cites6

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Cited by3

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