Theorems · Theorem · order theory
add_sub_div_two_lt
∀ {α : Type u_2} [inst : Field α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α] {a b : α},
a < b → a + (b - a) / 2 < b- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- add_commproof · cited by 1,535
- sub_eq_add_negproof · cited by 1,023
- add_assocproof · cited by 746
- PosMulReflectLTstatement and proof · cited by 278
- lt_sub_iff_add_ltproof · cited by 24
- zero_lt_two'proof · cited by 16
- div_lt_div_iff_of_pos_rightproof · cited by 15
- div_sub_div_sameproof · cited by 11
- sub_self_div_twoproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- exists_add_lt_and_pos_of_ltproof · cited by 1