[Merged by Bors] - feat(Algebra/Ring): generalise and extend material about sums of squares and semireal rings#16094
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[Merged by Bors] - feat(Algebra/Ring): generalise and extend material about sums of squares and semireal rings#16094
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…munity/mathlib4 into real_closed_field
…munity/mathlib4 into real_closed_field
YaelDillies
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Jan 15, 2025
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YaelDillies
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Jan 15, 2025
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Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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…res and semireal rings (#16094) * Generalise definition of a semireal ring, as discussed at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Formally.20real.20fields * Add facts about multiplicative structure of sums of squares -- preserved under multiplication, form a semiring, set of sums of squares is the semiring generated by the squares. * Add some lemmas to simpset * Update documentation Deletions: * `mem_sumSq_of_isSquare` (statement changed to `IsSquare.isSumSq`)
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Deletions:
mem_sumSq_of_isSquare(statement changed toIsSquare.isSumSq)This is work towards formalising some real algebra (see https://github.com/artie2000/real_closed_field).