Theorems · Theorem · order theory
Pi.colex_asc
∀ {ι : Type u_1} {α : Type u_3} [inst : Preorder ι] [inst_1 : DecidableEq ι] [inst_2 : LT α] {f : ι → α} {i j : ι},
i ≤ j → f i < f j → toColex (f ∘ ⇑(Equiv.swap i j)) < toColex fIf we swap two strictly increasing values in a function, then the result is colexicographically smaller than the original function.
- Defined in
- Mathlib.Order.PiLex
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderDecidableEqLT
Around this declaration
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.swapstatement · cited by 197
- Colexstatement · cited by 131
- toColexstatement and proof · cited by 90
- Equiv.swap_commproof · cited by 11
- Pi.lex_descproof · cited by 2
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