Theorems · Theorem · field theory
ArchimedeanClass.stdPart_sub_eq_right
∀ {K : Type u_1} [inst : LinearOrder K] [inst_1 : Field K] [inst_2 : IsOrderedRing K] {x y : K},
0 < ArchimedeanClass.mk x → ArchimedeanClass.stdPart (x - y) = -ArchimedeanClass.stdPart y- Defined in
- Mathlib.Algebra.Order.Ring.StandardPart
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- sub_eq_add_negproof · cited by 1,023
- IsOrderedRingstatement and proof · cited by 777
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- ArchimedeanClass.stdPartstatement and proof · cited by 42
- ArchimedeanClass.stdPart_negproof · cited by 5
- ArchimedeanClass.stdPart_add_eq_rightproof · cited by 2
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