Theorems · Theorem · commutative algebra
Field.DirectLimit.inv_mul_cancel
∀ {ι : Type u_1} [inst : Preorder ι] (G : ι → Type u_2) [inst_1 : Nonempty ι] [inst_2 : IsDirectedOrder ι]
[inst_3 : (i : ι) → Field (G i)] (f : (i j : ι) → i ≤ j → G i → G j) {p : Ring.DirectLimit G f},
p ≠ 0 → Field.DirectLimit.inv G f p * p = 1- Defined in
- Mathlib.Algebra.Colimit.Ring
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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- Preorderstatement and proof · cited by 7,952
- Fieldstatement and proof · cited by 7,404
- mul_commproof · cited by 2,262
- IsDirectedOrderstatement and proof · cited by 316
- Ring.DirectLimitstatement and proof · cited by 26
- Field.DirectLimit.invstatement and proof · cited by 2
- Field.DirectLimit.mul_inv_cancelproof · cited by 1
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