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Project-declaredLean 4.31.0 · mathlib@fabf563a7c95

Dappend eq add Cases

Fin.dappend_eq_addCases

Plain-language statement

dappend is equal to addCases. Marked as csimp to allow for switching to the addCases implementation during execution.

Exact Lean statement

@[csimp]
theorem dappend_eq_addCases : @dappend = @addCases

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
@[csimp]theorem dappend_eq_addCases : @dappend = @addCases := by  ext m n motive u v i  induction n with  | zero => simp [dappend, addCases, castLT]  | succ n ih =>    simp only [dappend, dconcat_eq_snoc]    have ih' :  (motive : Fin (m + n)  Sort _)      (u : (i : Fin m)  motive (castAdd n i))      (v : (i : Fin n)  motive (natAdd m i)),        dappend (motive := motive) u v = addCases (motive := motive) u v := by      intro motive_1 u_1 v_1      ext x : 1      apply ih    rw [ih' (fun i => motive i.castSucc) u (fun i => v (castSucc i))]    simp [snoc, addCases, last, castLT, subNat]    by_cases h : i.val < m    · have : i.val < m + n := by omega      simp [h, this]    · by_cases h' : i.val < m + n      · grind only      · have : i.val = m + n := by omega        grind only [cases Or]
Project
ArkLib
License
Apache-2.0
Commit
fad5cbf80877
Source
ArkLib/Data/Fin/Tuple/Lemmas.lean:340-362

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Project documentation

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Project-declaredLean 4.31.0

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Plain-language statement

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cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

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ArkLib.Lattices.Ajtai.gadgetDecompose_lawful

Plain-language statement

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Source project: ArkLib

Person-level attribution pending.

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