Theorems · Theorem · order theory
Order.lt_add_one_iff
∀ {α : Type u_1} {x y : α} [inst : LinearOrder α] [inst_1 : Add α] [inst_2 : One α] [SuccAddOrder α] [NoMaxOrder α],
x < y + 1 ↔ x ≤ y- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- NoMaxOrderstatement and proof · cited by 340
- SuccAddOrderstatement and proof · cited by 108
- not_isMaxproof · cited by 46
- Order.lt_add_one_iff_of_not_isMaxproof · cited by 2
Cited by13
Results whose statement or proof uses this declaration.
- Order.lt_two_iffproof · cited by 5
- Ordinal.isPrincipal_mul_iff_mul_left_eqproof · cited by 3
- Ordinal.log_eq_zeroproof · cited by 3
- Finset.sum_antidiagonal_choose_succ_nsmulproof · cited by 3
- Ordinal.log_eq_iffproof · cited by 2
- ZFSet.vonNeumann_add_oneproof · cited by 2
- MeasureTheory.measurableSet_prodMk_add_one_of_predictableproof · cited by 1
- Ordinal.lt_add_iff_of_isSuccLimitproof · cited by 1
- Topology.RelCWComplex.mem_skeleton_iffproof · cited by 1
- Nat.primeCounting_add_leproof · cited by 0
- Fin.sum_Iic_subproof · cited by 0
- PMF.binomial_apply_of_leproof · cited by 0