Theorems · Theorem · order theory
lt_update_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}, x < Function.update x i a ↔ x i < a- Defined in
- Mathlib.Order.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 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.
Cites2
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
Cited by2
Results whose statement or proof uses this declaration.
- Pi.lt_toLex_update_self_iffproof · cited by 1
- Pi.single_posproof · cited by 1