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Theorems · Theorem · logic and foundations

Cardinal.power_one

∀ (a : Cardinal.{u}), a ^ 1 = a
Defined in
Mathlib.SetTheory.Cardinal.Defs
Cited by
4 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Cardinal.pow_le · cited by 5Cardinal.pow_leCardinal.self_le_power · cited by 2Cardinal.self_le_powerCardinal.isPrimePow_iff · cited by 1Cardinal.isPrimePow_iffCardinal.powerlt_aleph0 · cited by 1Cardinal.powerlt_aleph0Cardinal · cited by 2598CardinalCardinal.mk_congr · cited by 55Cardinal.mk_congrEquiv.funUnique · cited by 22Equiv.funUniqueCardinal.inductionOn · cited by 19Cardinal.inductionOnCardinal.power_oneCITED BYCITES

Cites4

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

Cited by4

Results whose statement or proof uses this declaration.