def count_within

stelliferous@0.0.2.0 · proofs/bounded_u32_arithmetic.bend:11

import Base
import stelliferous@0.0.2.0/proofs/nat_to_u32_bounds.bend as Bounds
import stelliferous@0.0.2.0/proofs/nat_order.bend as Order
import stelliferous@0.0.2.0/proofs/u32_comparison.bend as Comparison

11def count_within(+count: U32,+length: Nat,+capacity: U32,+upper: U32,exact: {U32.to_nat(count) == length : Nat},
12  room: {Nat.is_le(length,U32.to_nat(capacity)) == True{} : Bool},capacity_bound: {U32.is_le(capacity,upper) == True{} : Bool}) ->
13  {U32.is_le(count,upper) == True{} : Bool}:
14  %Equal.sym(Bool,U32.is_le(count,upper),Nat.is_le(U32.to_nat(count),U32.to_nat(upper)),Comparison.le(count,upper)) : {_ == True{} : Bool}
15  %Equal.sym(Nat,U32.to_nat(count),length,exact) : {Nat.is_le(_,U32.to_nat(upper)) == True{} : Bool}
16  Order.transitive(length,U32.to_nat(capacity),U32.to_nat(upper),room,Bounds.as_nat_le(capacity,upper,capacity_bound))