Theorems · Theorem · commutative algebra
Subsemiring.closure_isSquare
∀ {T : Type u_2} [inst : CommSemiring T], Subsemiring.closure {x | IsSquare x} = Subsemiring.sumSq T- Defined in
- Mathlib.Algebra.Ring.SumsOfSquares
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Set.ofPredstatement and proof · cited by 6,101
- Subsemiringstatement · cited by 456
- IsSquarestatement and proof · cited by 132
- Subsemiring.closurestatement and proof · cited by 53
- Subsemiring.toNonUnitalSubsemiringproof · cited by 10
- NonUnitalSubsemiring.sumSqproof · cited by 6
- Submonoid.squareproof · cited by 5
- Subsemiring.sumSqstatement and proof · cited by 4
- Subsemiring.toNonUnitalSubsemiring_injectiveproof · cited by 2
- NonUnitalSubsemiring.closure_isSquareproof · cited by 1
- Submonoid.subsemiringClosure_toNonUnitalSubsemiringproof · cited by 1
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