Nat cast range card zmod of le
KZG.CommitmentScheme.nat_cast_range_card_zmod_of_le
Plain-language statement
Casting the first k ≤ p natural numbers into ZMod p is injective.
Exact Lean statement
lemma nat_cast_range_card_zmod_of_le {k : ℕ} (hk : k ≤ p) :
((Finset.range k).image ((↑) : ℕ → ZMod p)).card = kFormal artifact
Lean source
lemma nat_cast_range_card_zmod_of_le {k : ℕ} (hk : k ≤ p) : ((Finset.range k).image ((↑) : ℕ → ZMod p)).card = k := by have h_inj : Set.InjOn ((↑) : ℕ → ZMod p) ↑(Finset.range k) := by intro a ha b hb hab simp only [Finset.coe_range, Set.mem_Iio] at ha hb have hap : a < p := lt_of_lt_of_le ha hk have hbp : b < p := lt_of_lt_of_le hb hk have hv := congrArg ZMod.val hab rwa [ZMod.val_natCast_of_lt hap, ZMod.val_natCast_of_lt hbp] at hv rw [Finset.card_image_of_injOn h_inj, Finset.card_range]- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/Commitments/Functional/KZG/FunctionBinding/TauInQueries.lean:120-129
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Person-level attribution pending.
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Person-level attribution pending.
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Plain-language statement
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Source project: ArkLib
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