def ilog_bounds
bend-collections-laws-math@1.0.0.0 · proofs/math/natural/logs.bend:82
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/logs.bend as Logs
import Base
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/lemmas/proofs/nat_algebra.bend as A
82def ilog_bounds(+np: Nat, +bq: Nat) -> {Nat.is_le(Nat.pow(2n+bq, ilog_value(np, bq)), 1n+np) == True{} : Bool} & {Nat.is_lt(1n+np, Nat.pow(2n+bq, 1n+ilog_value(np, bq))) == True{} : Bool}:
83 ilog_ok(1n+np, 1n+np, bq, 0n, 1n, Nat.is_le(1n, Nat.div(1n+np, 2n+bq)), {==}, N.lt_succ_le_succ(0n, 1n+np, {==}), {==}, A.add_zero(1n+np))