def encoded_add_associative

stelliferous@0.0.2.0 · proofs/bounded_u32_arithmetic.bend:51

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

51# These are modular identities, so they require no no-overflow assumption.
52def encoded_add_associative(+a: Nat,+b: Nat,+c: Nat) ->
53  {((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}:
54  %Equal.sym(U32,(U32.from_nat(a) + U32.from_nat(b) : U32),U32.from_nat(Nat.add(a,b)),WordArithmetic.native_add(a,b)) :
55    {(_ + U32.from_nat(c) : U32) == (U32.from_nat(a) + (U32.from_nat(b) + U32.from_nat(c) : U32) : U32) : U32}
56  %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)) :
57    {_ == (U32.from_nat(a) + (U32.from_nat(b) + U32.from_nat(c) : U32) : U32) : U32}
58  %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}
59  %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}
60  %Addition.associative(a,b,c) : {U32.from_nat(Nat.add(Nat.add(a,b),c)) == U32.from_nat(_) : U32}
61  {==}