Theorems · Theorem · order theory
WithBot.coe_le_coe
∀ {α : Type u_1} {a b : α} [inst : LE α], ↑a ≤ ↑b ↔ a ≤ b- Defined in
- Mathlib.Order.WithBot
- Cited by
- 76 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- LE
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.
- WithBotstatement · cited by 1,498
- WithBot.somestatement · cited by 541
Cited by76
Results whose statement or proof uses this declaration.
- Polynomial.card_roots'proof · cited by 9
- WithZero.coe_le_coeproof · cited by 8
- Polynomial.modByMonic_X_sub_C_eq_C_evalproof · cited by 7
- Finset.sup'_le_iffproof · cited by 6
- Ideal.height_le_ringKrullDim_of_ne_topproof · cited by 5
- WithBot.preimage_coe_Iicproof · cited by 5
- Finset.le_sup'_iffproof · cited by 5
- Polynomial.degree_quadratic_leproof · cited by 4
- Module.length_compositionSeriesproof · cited by 4
- WithBot.preimage_coe_Iciproof · cited by 4
- Polynomial.trinomial_natDegreeproof · cited by 4
- Order.krullDim_eq_length_of_finiteDimensionalOrderproof · cited by 3