def right_restores_index_full

stelliferous@0.0.2.0 · proofs/storage_address_bounds.bend:48

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

48def right_restores_index_full(+depth: Nat,+index: U32,+limit: {Nat.is_le(1n+depth,31n) == True{} : Bool},+bound: {U32.is_lt(index,capacity(1n+depth)) == True{} : Bool},
49  +choice: {U32.is_lt(index,capacity(depth)) == False{} : Bool}) -> {U32.to_nat(index) == Nat.add(Shape.extent(depth),U32.to_nat((index - capacity(depth) : U32))) : Nat}:
50  %Equal.sym(Nat,U32.to_nat((index - capacity(depth) : U32)),Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth))),sub_value(depth,index,limit,bound,choice)) :
51    {U32.to_nat(index) == Nat.add(Shape.extent(depth),_) : Nat}
52  %capacity_value(depth,child_limit_full(depth,limit)) : {U32.to_nat(index) == Nat.add(_,Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth)))) : Nat}
53  Equal.sym(Nat,Nat.add(U32.to_nat(capacity(depth)),Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth)))),U32.to_nat(index),
54    Equal.trans(Nat,Nat.add(U32.to_nat(capacity(depth)),Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth)))),
55      Nat.add(Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth))),U32.to_nat(capacity(depth))),U32.to_nat(index),
56      Order.commutative(U32.to_nat(capacity(depth)),Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth)))),Subtraction.restore(U32.to_nat(index),U32.to_nat(capacity(depth)),right_order(depth,index,choice))))