[Merged by Bors] - feat(Analysis/Complex): If a = ∑ i ∈ s, f i and b = ∑ i ∈ s, (‖f i‖ : ℂ), then a ≤ b
#15022
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…‖ : ℂ)`, then `a ≤ b` This is a bit of a weird statement, but it is really useful when one wants to expand `‖f i‖ = ‖g i‖ ^ 2 = g i * conj (g i)` and do further complex number manipulations. It also avoids having to prove `a = ∑ i ∈ s, f i` twice: once for showing `0 ≤ a` and once in the goal. From LeanAPAP
PR summary 0dcafda52fImport changes for modified filesNo significant changes to the import graph Import changes for all files
Declarations diff
You can run this locally as follows## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>
## more verbose report:
./scripts/declarations_diff.sh long <optional_commit> |
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Thanks! bors r+ |
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…‖ : ℂ)`, then `a ≤ b` (#15022) This is a bit of a weird statement, but it is really useful when one wants to expand `‖f i‖ = ‖g i‖ ^ 2 = g i * conj (g i)` and do further complex number manipulations. It also avoids having to prove `a = ∑ i ∈ s, f i` twice: once for showing `0 ≤ a` and once in the goal. From LeanAPAP
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a = ∑ i ∈ s, f i and b = ∑ i ∈ s, (‖f i‖ : ℂ), then a ≤ ba = ∑ i ∈ s, f i and b = ∑ i ∈ s, (‖f i‖ : ℂ), then a ≤ b
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This is a bit of a weird statement, but it is really useful when one wants to expand
‖f i‖ = ‖g i‖ ^ 2 = g i * conj (g i)and do further complex number manipulations. It also avoids having to provea = ∑ i ∈ s, f itwice: once for showing0 ≤ aand once in the goal.From LeanAPAP