PROOF.u32.le_trans: def of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/PROOF.bend as PROOF
Lines 988-990 of bend-osdev-algo@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&start_line=988&end_line=990

import Base

def u32.le_trans(+a: U32, +b: U32, +c: U32, e: {U32.is_le(a, b) == True{} : Bool}, f: {U32.is_le(b, c) == True{} : Bool}) -> {U32.is_le(a, c) == True{} : Bool}:
  %Equal.sym(Cmp, U32.cmp(a, c), Nat.cmp(U32.to_nat(a), U32.to_nat(c)), u32.cmp_nat(a, c)) : {Cmp.is_le(_) == True{} : Bool}
  nat.le_trans(U32.to_nat(a), U32.to_nat(b), U32.to_nat(c), u32.mv_le(a, b, True{}, e), u32.mv_le(b, c, True{}, f))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=nat.le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=u32.cmp_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=u32.mv_le