Theorems · Theorem · order theory
one_sub_le_one_sub_mul_one_add
∀ {R : Type u} [inst : Ring R] [inst_1 : PartialOrder R] [IsOrderedRing R] {a b c : R},
b + b * c ≤ a + c → 1 - a ≤ (1 - b) * (1 + c)- Defined in
- Mathlib.Algebra.Order.Ring.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, 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.
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- le_reflproof · cited by 2,061
- add_commproof · cited by 1,535
- IsOrderedRingstatement and proof · cited by 777
- add_assocproof · cited by 746
- add_le_addproof · cited by 666
- mul_one_addproof · cited by 6
- one_sub_mulproof · cited by 5
- sub_le_sub_iffproof · cited by 2
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