Mathlib Map

Theorems · Theorem · group theory

AddUnits.isAddUnit_add_addUnits

∀ {M : Type u_1} [inst : AddMonoid M] (a : M) (u : AddUnits M), IsAddUnit (a + ↑u) ↔ IsAddUnit a

Addition of a u : AddUnits M on the right doesn't affect IsAddUnit.

Defined in
Mathlib.Algebra.Group.Units.Defs
Cited by
1 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Assumes
AddMonoid
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Around this declaration

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

addIrreducible_add_addUnits · cited by 1addIrreducible_add_addUni…AddMonoid · cited by 2864AddMonoidadd_zero · cited by 2707add_zeroadd_assoc · cited by 746add_assocAddUnits · cited by 325AddUnitsAddUnits.val · cited by 248AddUnits.valIsAddUnit · cited by 215IsAddUnitAddUnits.add_neg · cited by 19AddUnits.add_negAddUnits.isAddUnit · cited by 14AddUnits.isAddUnitIsAddUnit.add · cited by 11IsAddUnit.addAddUnits.val_add · cited by 5AddUnits.val_addAddUnits.isAddUnit_add_addUni…CITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.