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proof(SafeJson): DISCHARGE appendLengthInc via lengthSnoc + plusCommutative (proven#90 #107 #119) #127

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Merged
hyperpolymath merged 1 commit into from
May 30, 2026
+13 −4
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proof(SafeJson): DISCHARGE appendLengthInc via lengthSnoc + plusCommutative (proven#90 #107 #119) #127

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17 changes: 13 additions & 4 deletions src/Proven/SafeJson/Proofs.idr
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Original file line number Diff line number Diff line change
Expand Up @@ -9,7 +9,9 @@ module Proven.SafeJson.Proofs
import Proven.Core
import Proven.SafeJson
import Data.List
import Data.List.Equalities
import Data.List.Quantifiers
import Data.Nat

%default total

Expand Down Expand Up @@ -193,10 +195,17 @@ prependLengthInc v arr = Refl
||| `Data.List.lengthAppendSingleton` lemma. Discharge by composing
||| `lengthAppend` + `plusZeroRightNeutral` + `S` congruence, or by
||| adding a direct singleton-append lemma to base.
public export
0 appendLengthInc : (v : JsonValue) -> (arr : List JsonValue) ->
arrayLength (append v (JsonArray arr)) =
Just (length arr + 1)
||| DISCHARGED: `append v (JsonArray arr) = JsonArray (arr ++ [v])`
||| (SafeJson.idr L233-234), so the goal reduces to
||| `Just (length (arr ++ [v])) = Just (length arr + 1)`. Apply
||| `lengthSnoc arr v : length (arr ++ [v]) = S (length arr)`, then
||| close the `S n` vs `n + 1` gap with `plusCommutative 1 n`.
public export
appendLengthInc : (v : JsonValue) -> (arr : List JsonValue) ->
arrayLength (append v (JsonArray arr)) =
Just (length arr + 1)
appendLengthInc v arr =
cong Just (trans (lengthSnoc arr v) (plusCommutative 1 (length arr)))

--------------------------------------------------------------------------------
-- Path Access Properties
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