BoundedU32Arithmetic.count_within: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend as BoundedU32Arithmetic
Lines 11-16 of stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/bounded_u32_arithmetic.bend&start_line=11&end_line=16

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

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

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=transitive
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_to_u32_bounds.bend&name=as_nat_le
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/u32_comparison.bend&name=le