U32alg.sc_add: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend as U32alg
Lines 47-53 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend&start_line=47&end_line=53

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

def sc_add(+n: Nat, +x: Nat, +y: Nat) -> {Nat.add(sc(n, x), sc(n, y)) == sc(n, Nat.add(x, y)) : Nat}:
  match n:
    case 0n:
      {==}
    case 1n+p:
      %Equal.sym(Nat, Nat.add(Nat.double(sc(p, x)), Nat.double(sc(p, y))), Nat.double(Nat.add(sc(p, x), sc(p, y))), N.add_double(sc(p, x), sc(p, y))) : {_ == Nat.double(sc(p, Nat.add(x, y))) : Nat}
      Equal.cong(Nat, Nat, Nat.double, Nat.add(sc(p, x), sc(p, y)), sc(p, Nat.add(x, y)), sc_add(p, x, y))

Uses (7):
  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.sym
  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
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.double
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_double
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32alg.bend&name=sc