Theorems · Theorem · order theory
le_update_iff
∀ {ι : Type u_1} {π : ι → Type u_4} [inst : DecidableEq ι] [inst_1 : (i : ι) → Preorder (π i)] {x y : (i : ι) → π i}
{i : ι} {a : π i}, x ≤ Function.update y i a ↔ x i ≤ a ∧ ∀ (j : ι), j ≠ i → x j ≤ y j- Defined in
- Mathlib.Order.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 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.
Cites3
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
- Function.forall_update_iffproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- single_mem_stdSimplexproof · cited by 10
- Finset.induction_on_pi_of_choiceproof · cited by 2
- isLUB_piproof · cited by 0
- TopologicalSpace.nhds_mkOfNhds_singleproof · cited by 0