norm_num extensions for Nat.log and Nat.clog

This module defines norm_num extensions for Nat.log and Nat.clog.

def Mathlib.Meta.NormNum.proveNatLog (eb en : Q(ℕ)) : (ek : Q(ℕ)) × Q(Nat.log «$eb» «$en» = «$ek»)

Given the natural number literals eb and en, returns Nat.log eb en as a natural number literal and an equality proof. Panics if ex or en aren't natural number literals.

def Mathlib.Meta.NormNum.evalNatLog : NormNumExt

Evaluates the Nat.log function.

theorem Mathlib.Meta.NormNum.nat_clog_helper {b m n : ℕ} (hb : Nat.blt 1 b = true) (h₁ : (b ^ m).blt n = true) (h₂ : n.ble (b ^ (m + 1)) = true) : Nat.clog b n = m + 1

def Mathlib.Meta.NormNum.proveNatClog (eb en : Q(ℕ)) : (ek : Q(ℕ)) × Q(Nat.clog «$eb» «$en» = «$ek»)

Given the natural number literals eb and en, returns Nat.clog eb en as a natural number literal and an equality proof. Panics if ex or en aren't natural number literals.

def Mathlib.Meta.NormNum.evalNatClog : NormNumExt

Evaluates the Nat.clog function.