Theorems · Theorem · Lie groups
NonarchimedeanRing.mul_subset
∀ {R : Type u_1} [inst : Ring R] [inst_1 : TopologicalSpace R] [NonarchimedeanRing R] (U : OpenAddSubgroup R),
∃ V, ↑V * ↑V ⊆ ↑UAn open subgroup of a nonarchimedean ring contains the square of another one.
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- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Set.preimageproof · cited by 4,946
- MulZeroClass.mul_zeroproof · cited by 2,091
- SProd.sprodproof · cited by 1,750
- IsOpen.mem_nhdsproof · cited by 470
- SetLike.mem_coeproof · cited by 302
- Set.mulstatement · cited by 297
- IsOpen.preimageproof · cited by 147
- OpenAddSubgroupstatement and proof · cited by 47
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