[Merged by Bors] - chore(Topology/PartitionOfUnity): shorten proof using ParitionOfUnity.le_one #19899
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PR summary 5a6c9a4629Import changes for modified filesNo significant changes to the import graph Import changes for all files
Declarations diffNo declarations were harmed in the making of this PR! 🐙 You can run this locally as follows## summary with just the declaration names:
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| · exact fun j _ _ => f.nonneg j x | ||
| simp only [Finset.singleton_subset_iff, Finset.mem_filter, Finset.mem_univ, true_and] | ||
| exact h0 | ||
| exact ⟨f.nonneg i x, PartitionOfUnity.le_one f i x⟩ |
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The type required for the second component here is (f i) x ≤ 1, which is exactly what PartitionOfUnity.le_one gives us. (No defeq shenanigans.)
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🚀 Pull request has been placed on the maintainer queue by tb65536. |
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Thanks! 🎉 |
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….le_one (#19899) Replaces 11 lines of proof with a single invocation of [`ParitionOfUnity.le_one`](https://github.com/leanprover-community/mathlib4/blob/4411562e4fd2d02aa31e413bc8e948829aa3a62d/Mathlib/Topology/PartitionOfUnity.lean#L171). I observed this (via `set_option trace.profiler true`) to lower the elaboration time of this theorem from 0.20 seconds to 0.08 seconds. This simplification was found by [`tryAtEachStep`](https://github.com/dwrensha/tryAtEachStep).
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Replaces 11 lines of proof with a single invocation of
ParitionOfUnity.le_one.I observed this (via
set_option trace.profiler true) to lower the elaboration time of this theorem from 0.20 seconds to 0.08 seconds.This simplification was found by
tryAtEachStep.