List.sorted_head_le_mem: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 1012-1019 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=1012&end_line=1019

import Base
import bend-mathlib@0.8.1.0/nat.bend as MNat

# The head of a Nat list sorted by Nat.is_le is <= every member of its tail.
law sorted_head_le_mem:
  for x: Nat
  for xs: List<&2, Nat>
  for y: Nat
  for hs: sorted_by(~Nat, ~Nat.is_le, x <> xs)
  for hm: mem(~Nat, ~Nat.is_eq, y, xs)
  MNat.le(x, y)

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=internal_head_le_mem
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=mem
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=sorted_by
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=le