refactor(Analysis/Calculus/FormalMultilinearSeries): generalize to additive monoids #9467
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…ditive monoids While many of the lemmas cease to apply, the definitions of sequences and their sums are still perfectly well-behaved in additive monoids; no negation is needed. We could use this to generalize `NormedSpace.exp` such that it works with `NNReal`, but unless leanprover-community/mathlib3#16554 or similar lands and provides a `DivisionSemiring.nnqsmul` field, that would conflict with #8370.
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Here are the benchmark results for commit ee16fce. Benchmark Metric Change
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- ~Mathlib.Analysis.Analytic.Basic instructions 12.0%
- ~Mathlib.Analysis.Analytic.CPolynomial instructions 13.2%
- ~Mathlib.Analysis.Calculus.ContDiff.Basic instructions 6.5%
- ~Mathlib.Analysis.Calculus.ContDiff.Defs instructions 10.3%
+ ~Mathlib.Analysis.Calculus.FormalMultilinearSeries instructions -14.6% |
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While many of the lemmas cease to apply,
the definitions of sequences and their sums are still perfectly well-behaved in additive monoids; no negation is needed.
In future, we could use this to generalize
NormedSpace.expsuch that it works withNNReal, but unless leanprover-community/mathlib3#16554 or similar lands and provides aDivisionSemiring.nnqsmulfield, that would conflict with #8370.This also adds a new
sub_applylemma for good measure.