List.take_append: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 1108-1115 of bend-mathlib@0.8.1.0/list.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/list.bend&start_line=1108&end_line=1115
import Base
# Taking past the first part of an append keeps it and takes the rest from the second part.
law take_append:
for -a: Quant
for -A: Kind(a)
for xs: List
for -ys: List
for -n: Nat
{List.take(a, A, List.append(a, A, xs, ys), Nat.add(List.length(a, A, xs), n)) == List.append(a, A, xs, List.take(a, A, ys, n)) : List}
Uses (6):
https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add