Wrappers.int_range_bounds: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/wrappers.bend as Wrappers
Lines 265-273 of bend-collections-laws-math@1.0.0.0/proofs/math/random/wrappers.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/wrappers.bend&start_line=265&end_line=273

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/random.bend as SRM
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as W
import bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L

def int_range_bounds(~S: Data, ~next: S -> W.U64 & S, +s: S, +lo: Nat, +hi: Nat, +h: {Nat.is_lt(lo, hi) == True{} : Bool}, +hw: {C.fits(64n, Nat.sub(hi, lo)) == True{} : Bool}) -> SRM.IntRange.bounds(~S, ~next, s, lo, hi, h, hw):
  +d = Nat.sub(hi, lo)
  +k = R.fst(Nat, S, R.intn(~S, ~next, s, d))
  hk = intn_lt(~S, ~next, s, d, lt_pos(lo, hi, h), hw)
  +up = Equal.trans(Bool, Nat.is_lt(Nat.add(lo, k), hi), Nat.is_lt(Nat.add(lo, k), Nat.add(lo, d)), True{},
    Equal.cong(Nat, Bool, z => Nat.is_lt(Nat.add(lo, k), z), hi, Nat.add(lo, d), Equal.sym(Nat, Nat.add(lo, d), hi, N.sub_add(hi, lo, N.lt_le(lo, hi, h)))),
    N.lt_add_left(k, d, lo, hk))
  %Equal.sym(Nat, R.fst(Nat, S, R.plus(S, lo, R.intn(~S, ~next, s, d))), Nat.add(lo, k), plus_fst(S, lo, R.intn(~S, ~next, s, d))) : {Bool.and(Nat.is_le(lo, _), Nat.is_lt(_, hi)) == True{} : Bool}
  L.and_intro(Nat.is_le(lo, Nat.add(lo, k)), Nat.is_lt(Nat.add(lo, k), hi), N.le_add_right(lo, k), up)

Uses (25):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  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=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=and_intro
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=le_add_right
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_add_left
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=lt_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=sub_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/wrappers.bend&name=intn_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/wrappers.bend&name=lt_pos
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/wrappers.bend&name=plus_fst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=fits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random.bend&name=IntRange.bounds
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=fst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=intn
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend&name=plus
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64