def sub_value

stelliferous@0.0.2.0 · proofs/storage_address_bounds.bend:42

import Base
import stelliferous@0.0.2.0/proofs/word_power_of_two.bend as Power
import stelliferous@0.0.2.0/proofs/nat_order.bend as Order
import stelliferous@0.0.2.0/proofs/nat_to_u32_bounds.bend as Bounds
import stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend as Arithmetic

42def sub_value(+depth: Nat,+index: U32,+limit: {Nat.is_le(1n+depth,31n) == True{} : Bool},+bound: {U32.is_lt(index,capacity(1n+depth)) == True{} : Bool},
43  choice: {U32.is_lt(index,capacity(depth)) == False{} : Bool}) -> {U32.to_nat((index - capacity(depth) : U32)) == Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth))) : Nat}:
44  Arithmetic.subtract(index,capacity(depth),capacity(1n+depth),Power.native_power_bound(1n+depth,limit),right_order(depth,index,choice),
45    Order.transitive(Nat.sub(U32.to_nat(index),U32.to_nat(capacity(depth))),U32.to_nat(index),U32.to_nat(capacity(1n+depth)),
46      Order.sub_le(U32.to_nat(index),U32.to_nat(capacity(depth))),Bounds.strict_le(U32.to_nat(index),U32.to_nat(capacity(1n+depth)),Bounds.as_nat_lt(index,capacity(1n+depth),bound))))