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Theorems · Theorem · group theory

addIrreducible_addUnits_add

∀ {M : Type u_2} [inst : AddMonoid M] {y : M} (u : AddUnits M), AddIrreducible (↑u + y) ↔ AddIrreducible y
Defined in
Mathlib.Algebra.Group.Irreducible.Lemmas
Cited by
1 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext
Assumes
AddMonoid
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Around this declaration

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

addIrreducible_isAddUnit_add · cited by 1addIrreducible_isAddUnit_…AddMonoid · cited by 2864AddMonoidadd_assoc · cited by 746add_assocAddUnits · cited by 325AddUnitsAddUnits.val · cited by 248AddUnits.valIsAddUnit · cited by 215IsAddUnitAddIrreducible · cited by 24AddIrreducibleAddUnits.neg_add_cancel_left · cited by 8AddUnits.neg_add_cancel_l…addIrreducible_iff · cited by 6addIrreducible_iffAddUnits.isAddUnit_addUnits_add · cited by 1AddUnits.isAddUnit_addUni…addIrreducible_addUnits_addCITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.