def branch_total

stelliferous@0.0.2.0 · proofs/binary_division.bend:81

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

81def branch_total(+g: Bool,+q: Nat,+s: Nat,+b: Nat,guard: {Nat.is_ge(s,b) == g : Bool}) -> {total(branch(g,q,s,b),b) == Nat.add(Nat.mul(q,b),s) : Nat}:
82  match g:
83    case False{}:
84      {==}
85    case True{}:
86      %Equal.sym(Nat,Nat.add(Nat.add(b,Nat.mul(q,b)),Nat.sub(s,b)),Nat.add(Nat.mul(q,b),Nat.add(Nat.sub(s,b),b)),rotate(b,Nat.mul(q,b),Nat.sub(s,
87            b))) : {_ == Nat.add(Nat.mul(q,b),s) : Nat}
88      %Subtraction.restore(s,b,Order.ge_true(s,b,guard)) : {Nat.add(Nat.mul(q,b),Nat.add(Nat.sub(s,b),b)) == Nat.add(Nat.mul(q,b),_) : Nat}
89      {==}