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Theorems · Theorem · logic and foundations

Cardinal.add_one_lt_of_lt

∀ {a b : Cardinal.{u_1}}, Cardinal.aleph0 ≤ b → a < b → a + 1 < b
Defined in
Mathlib.SetTheory.Cardinal.Arithmetic
Cited by
1 results in Mathlib
Foundations
Depth 103 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.mk_Iic_lt · cited by 2Cardinal.mk_Iic_ltCardinal · cited by 2598CardinalLT.lt.trans_le · cited by 678lt.trans_leCardinal.aleph0 · cited by 521Cardinal.aleph0Cardinal.one_lt_aleph0 · cited by 20Cardinal.one_lt_aleph0Cardinal.add_lt_of_lt · cited by 7Cardinal.add_lt_of_ltCardinal.add_one_lt_of_ltCITED BYCITES

Cites5

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Cited by1

Results whose statement or proof uses this declaration.