Theorems · Theorem · order theory
Pi.trichotomous_lex
∀ {ι : Type u_1} {β : ι → Type u_2} (r : ι → ι → Prop) (s : {i : ι} → β i → β i → Prop) [∀ (i : ι), Std.Trichotomous s],
WellFounded r → Std.Trichotomous (Pi.Lex r s)- Defined in
- Mathlib.Order.PiLex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Std.Trichotomous
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- Function.ne_iffproof · cited by 40
- WellFounded.minproof · cited by 33
- Not.imp_symmproof · cited by 25
- WellFounded.min_memproof · cited by 23
- WellFounded.not_lt_minproof · cited by 20
- Pi.Lexstatement and proof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Pi.isTrichotomous_lexproof · cited by 0