Theorems · Theorem · order theory
card_Ico_one_mul
∀ {M : Type u_1} [inst : CancelCommMonoid M] [inst_1 : LinearOrder M] [IsOrderedMonoid M]
[inst_3 : LocallyFiniteOrder M] [ExistsMulOfLE M] (a b : M),
1 ≤ a → 1 ≤ b → (Finset.Ico 1 (a * b)).card = (Finset.Ico 1 a).card + (Finset.Ico 1 b).card- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- one_mulproof · cited by 2,841
- Finset.cardstatement and proof · cited by 2,327
- add_commproof · cited by 1,535
- LocallyFiniteOrderstatement and proof · cited by 658
- IsOrderedMonoidstatement and proof · cited by 577
- Finset.Icostatement and proof · cited by 450
- inf_of_le_leftproof · cited by 186
- sup_of_le_rightproof · cited by 143
- tsub_zeroproof · cited by 123
- CancelCommMonoidstatement and proof · cited by 23
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