def subtract_zero

stelliferous@0.0.2.0 · proofs/bounded_u32_arithmetic.bend:113

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

113def subtract_zero(+value: U32) -> {(value - 0 : U32) == value : U32}:
114  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))),
115    Equal.trans(U32,U32.from_nat(Nat.sub(U32.to_nat(value),0n)),U32.from_nat(U32.to_nat(value)),value,
116      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)))