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Theorems · Theorem · order theory

BooleanRing.mul_self

∀ {α : Type u_1} [inst : BooleanRing α] (a : α), a * a = a
Defined in
Mathlib.Algebra.Ring.BooleanRing
Cited by
7 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
BooleanRing
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Around this declaration

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

BooleanRing.add_self · cited by 6BooleanRing.add_selfBooleanRing.le_sup_inf_aux · cited by 1BooleanRing.le_sup_inf_auxBooleanRing.inf_sup_self · cited by 0BooleanRing.inf_sup_selfBooleanRing.sup_inf_self · cited by 0BooleanRing.sup_inf_selfBooleanRing.le_sup_inf · cited by 0BooleanRing.le_sup_infBooleanRing.mul_add_mul · cited by 0BooleanRing.mul_add_mulBooleanRing.mul_one_add_self · cited by 0BooleanRing.mul_one_add_s…IsIdempotentElem.eq · cited by 42IsIdempotentElem.eqBooleanRing · cited by 38BooleanRingBooleanRing.isIdempotentElem · cited by 1BooleanRing.isIdempotentE…BooleanRing.mul_selfCITED BYCITES

Cites3

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

Cited by7

Results whose statement or proof uses this declaration.