Theorems · Theorem · order theory
WithTop.coe_lt_coe
∀ {α : Type u_1} {a b : α} [inst : LT α], ↑b < ↑a ↔ b < a- Defined in
- Mathlib.Order.WithBot
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- LT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- WithTopstatement · cited by 3,754
- WithTop.somestatement · cited by 1,128
- WithTop.coe_ne_topproof · cited by 43
- WithTop.coe_injproof · cited by 21
- WithTop.lt_def'proof · cited by 4
Cited by47
Results whose statement or proof uses this declaration.
- ENNReal.coe_lt_coeproof · cited by 44
- HahnSeries.coeff_eq_zero_of_lt_orderTopproof · cited by 9
- WithTop.coe_strictMonoproof · cited by 8
- MvPowerSeries.coeff_eq_zero_of_lt_lexOrderproof · cited by 5
- WithTop.preimage_coe_Ioiproof · cited by 5
- Polynomial.coeff_eq_zero_of_lt_natTrailingDegreeproof · cited by 5
- WithTop.preimage_coe_Iioproof · cited by 4
- WithTop.strictMono_iffproof · cited by 4
- meromorphicOrderAt_add_eq_left_of_ltproof · cited by 3
- WithTop.untop_lt_iffproof · cited by 3
- WithTop.iSup_coe_eq_topproof · cited by 3
- WithTop.coe_lt_zeroproof · cited by 2