Theorems · Theorem · order theory
toZ_of_ge
∀ {ι : Type u_1} [inst : LinearOrder ι] [inst_1 : SuccOrder ι] [inst_2 : IsSuccArchimedean ι] [inst_3 : PredOrder ι]
{i0 i : ι} (hi : i0 ≤ i), toZ i0 i = ↑(Nat.find ⋯)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Nat.iteratestatement · cited by 740
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- PredOrderstatement and proof · cited by 334
- Nat.findstatement · cited by 139
- IsSuccArchimedeanstatement and proof · cited by 88
- toZstatement · cited by 23
- IsSuccArchimedean.exists_succ_iterate_of_lestatement · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- iterate_succ_toZproof · cited by 2
- toZ_of_eqproof · cited by 2
- toZ_nonnegproof · cited by 1
- toZ_iterate_succ_of_not_isMaxproof · cited by 1
- toZ_iterate_succ_leproof · cited by 0