Theorems · Theorem · order theory
sub_nonpos
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddRightMono α] {a b : α}, a - b ≤ 0 ↔ a ≤ b- Cited by
- 29 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddGroupLEAddRightMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- zero_addproof · cited by 2,366
- sub_eq_add_negproof · cited by 1,023
- AddRightMonostatement and proof · cited by 367
- neg_add_cancel_rightproof · cited by 75
- add_le_add_iff_rightproof · cited by 47
Cited by29
Results whose statement or proof uses this declaration.
- sub_nonpos_of_leproof · cited by 5
- Real.sin_eq_zero_iffproof · cited by 5
- Real.smoothTransition.one_of_one_leproof · cited by 3
- Real.dist_le_of_mem_Iccproof · cited by 3
- max_sub_min_eq_abs'proof · cited by 3
- IsLocalMaxOn.hasFDerivWithinAt_nonposproof · cited by 3
- abs_sub_le_max_subproof · cited by 2
- StieltjesFunction.length_Iocproof · cited by 2
- MeasureTheory.posConvolution_eq_convolution_indicatorproof · cited by 2
- mul_sub_mul_div_mul_nonpos_iffproof · cited by 2
- exists_hasDerivWithinAt_eq_of_gt_of_ltproof · cited by 2
- CauSeq.sup_eq_rightproof · cited by 2