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ctchou
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Apr 7, 2026
| namespace Cslib.FinFun | ||
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| /-- `FinFun` equivalent of `Function.update`. -/ | ||
| def update [Zero β] [DecidableEq α] [∀ b : β, Decidable (b = 0)] (f : α →₀ β) (a : α) (b : β) : |
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I wonder if it is worthwhile to introduce a DecidableEqZero class, as the pattern [∀ b : β, Decidable (b = 0)] appears so many times in FinFun.
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| /-- Updating a function with a nonempty element yields the same support with, possibly, the addition | ||
| of the key. -/ | ||
| @[scoped grind .] | ||
| theorem update_neq_zero_support_eq_union [Zero β] [DecidableEq α] [∀ b : β, Decidable (b = 0)] | ||
| (f : α →₀ β) (h : b ≠ 0) : | ||
| (f.update a b).support = f.support ∪ {a} := by grind | ||
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| /-- Updating a key in the support with a nonempty element preserves the support. -/ | ||
| theorem update_neq_zero_support_eq [Zero β] [DecidableEq α] [∀ b : β, Decidable (b = 0)] | ||
| (f : α →₀ β) (h₁ : f a ≠ 0) (h₂ : b ≠ 0) : (f.update a b).support = f.support := by grind |
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Are these two theorems really necessary given update_support above?
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This PR adds
FinFun.updateand proves some basic results about the functional interface and support of the resulting function.