Theorems · Theorem · order theory
PosMulReflectLT.toPosMulStrictMono
∀ (G₀ : Type u_3) [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀], PosMulStrictMono G₀
For a group with zero, PosMulReflectLT G₀ implies PosMulStrictMono G₀.
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- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- GroupWithZerostatement and proof · cited by 691
- PosMulReflectLTstatement and proof · cited by 278
- PosMulStrictMonostatement · cited by 151
- inv_pos_of_posproof · cited by 123
- inv_mul_cancel_left₀proof · cited by 47
- lt_of_mul_lt_mul_leftproof · cited by 15
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