BoundedU32Arithmetic.encoded_add_associative: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend as BoundedU32Arithmetic
Lines 51-61 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=51&end_line=61

import Base
import stelliferous@0.0.2.0/proofs/word_arithmetic.bend as WordArithmetic
import stelliferous@0.0.2.0/proofs/natural_addition.bend as Addition

# These are modular identities, so they require no no-overflow assumption.
def encoded_add_associative(+a: Nat,+b: Nat,+c: Nat) ->
  {((U32.from_nat(a) + U32.from_nat(b) : U32) + U32.from_nat(c) : U32) == (U32.from_nat(a) + (U32.from_nat(b) + U32.from_nat(c) : U32) : U32) : U32}:
  %Equal.sym(U32,(U32.from_nat(a) + U32.from_nat(b) : U32),U32.from_nat(Nat.add(a,b)),WordArithmetic.native_add(a,b)) :
    {(_ + U32.from_nat(c) : U32) == (U32.from_nat(a) + (U32.from_nat(b) + U32.from_nat(c) : U32) : U32) : U32}
  %Equal.sym(U32,(U32.from_nat(Nat.add(a,b)) + U32.from_nat(c) : U32),U32.from_nat(Nat.add(Nat.add(a,b),c)),WordArithmetic.native_add(Nat.add(a,b),c)) :
    {_ == (U32.from_nat(a) + (U32.from_nat(b) + U32.from_nat(c) : U32) : U32) : U32}
  %Equal.sym(U32,(U32.from_nat(b) + U32.from_nat(c) : U32),U32.from_nat(Nat.add(b,c)),WordArithmetic.native_add(b,c)) : {U32.from_nat(Nat.add(Nat.add(a,b),c)) == (U32.from_nat(a) + _ : U32) : U32}
  %Equal.sym(U32,(U32.from_nat(a) + U32.from_nat(Nat.add(b,c)) : U32),U32.from_nat(Nat.add(a,Nat.add(b,c))),WordArithmetic.native_add(a,Nat.add(b,c))) : {U32.from_nat(Nat.add(Nat.add(a,b),c)) == _ : U32}
  %Addition.associative(a,b,c) : {U32.from_nat(Nat.add(Nat.add(a,b),c)) == U32.from_nat(_) : U32}
  {==}

Uses (8):
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/natural_addition.bend&name=associative
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_arithmetic.bend&name=native_add