F64sqa.ilt: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqa.bend as F64sqa
Lines 22-23 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqa.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqa.bend&start_line=22&end_line=23

import Base
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/sqrtn.bend as SQ

def ilt(+n: Nat) -> {Nat.is_lt(n, Nat.mul(1n+M.isqrt(n), 1n+M.isqrt(n))) == True{} : Bool}:
  L.subst(Nat, z => {Nat.is_lt(n, z) == True{} : Bool}, Nat.pow(1n+M.isqrt(n), 2n), Nat.mul(1n+M.isqrt(n), 1n+M.isqrt(n)), sqm(1n+M.isqrt(n)), SQ.lt_succ_isqrt(n))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/sqrtn.bend&name=lt_succ_isqrt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64sqa.bend&name=sqm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=isqrt