Theorems · Theorem · order theory
update_lt_self_iff
∀ {ι : Type u_1} {π : ι → Type u_4} [inst : DecidableEq ι] [inst_1 : (i : ι) → Preorder (π i)] {x : (i : ι) → π i}
{i : ι} {a : π i}, Function.update x i a < x ↔ a < x i- Defined in
- Mathlib.Order.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqPreorder
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.
- Preorderstatement and proof · cited by 7,952
- Function.updatestatement · cited by 502
- lt_iff_le_not_geproof · cited by 35
- le_update_self_iffproof · cited by 2
- update_le_self_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Pi.toLex_update_lt_self_iffproof · cited by 1