BoundedU32Arithmetic.subtract_zero: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend as BoundedU32Arithmetic
Lines 113-116 of stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend&start_line=113&end_line=116

import Base
import stelliferous@0.0.2.0/proofs/nat_order.bend as Order

def subtract_zero(+value: U32) -> {(value - 0 : U32) == value : U32}:
  Equal.trans(U32,(value - 0 : U32),U32.from_nat(Nat.sub(U32.to_nat(value),0n)),value,native_subtract(value,0,Order.zero_le(U32.to_nat(value))),
    Equal.trans(U32,U32.from_nat(Nat.sub(U32.to_nat(value),0n)),U32.from_nat(U32.to_nat(value)),value,
      Equal.cong(Nat,U32,U32.from_nat,Nat.sub(U32.to_nat(value),0n),U32.to_nat(value),Order.subtract_zero(U32.to_nat(value))),native_roundtrip(value)))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend&name=native_roundtrip
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend&name=native_subtract
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=subtract_zero
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=zero_le