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Theorems · Theorem · order theory

sub_lt_zero

∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddRightStrictMono α] {a b : α}, a - b < 0 ↔ a < b

Alias of sub_neg. For a - -b = a + b, see sub_neg_eq_add.

Defined in
Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by
4 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext
Assumes
AddGroupLTAddRightStrictMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

mul_sub_mul_div_mul_neg_iff · cited by 2mul_sub_mul_div_mul_neg_i…exists_hasDerivWithinAt_eq_of_gt_of_lt · cited by 2exists_hasDerivWithinAt_e…ZMod.valMinAbs_nonneg_iff · cited by 1ZMod.valMinAbs_nonneg_iffriemannZeta_one_ne_zero · cited by 1riemannZeta_one_ne_zeroAddGroup · cited by 4410AddGroupAddRightStrictMono · cited by 160AddRightStrictMonosub_neg · cited by 22sub_negsub_lt_zeroCITED BYCITES

Cites3

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Cited by4

Results whose statement or proof uses this declaration.