Theorems · Theorem · order theory
map_pos_of_ne_zero
∀ {F : Type u_2} {α : Type u_3} {β : Type u_4} [inst : FunLike F α β] [inst_1 : AddGroup α] [inst_2 : AddCommMonoid β]
[inst_3 : LinearOrder β] [IsOrderedAddMonoid β] [AddGroupNormClass F α β] (f : F) {x : α}, x ≠ 0 → 0 < f x- Defined in
- Mathlib.Algebra.Order.Hom.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- LinearOrderstatement and proof · cited by 8,572
- AddGroupstatement and proof · cited by 4,410
- FunLikestatement and proof · cited by 2,560
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- LE.le.lt_of_neproof · cited by 116
- NonnegHomClass.apply_nonnegproof · cited by 79
- AddGroupNormClassstatement and proof · cited by 6
- map_ne_zero_iff_ne_zeroproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Rat.AbsoluteValue.is_prime_of_minimal_nat_zero_lt_and_lt_oneproof · cited by 3
- Rat.AbsoluteValue.equiv_real_of_unboundedproof · cited by 1
- Rat.AbsoluteValue.exists_minimal_nat_zero_lt_and_lt_oneproof · cited by 1