chore(*): add mathlib4 synchronization comments (#19238)

Regenerated from the [port status wiki page](https://github.com/leanprover-community/mathlib/wiki/mathlib4-port-status).
Relates to the following files:
* `algebra.expr`
* `algebraic_geometry.morphisms.finite_type`
* `algebraic_geometry.morphisms.ring_hom_properties`
* `arithcc`
* `canonically_ordered_comm_semiring_two_mul`
* `char_p_zero_ne_char_zero`
* `cyclotomic_105`
* `data.matrix.auto`
* `direct_sum_is_internal`
* `examples.mersenne_primes`
* `examples.prop_encodable`
* `geometry.manifold.instances.sphere`
* `girard`
* `homogeneous_prime_not_prime`
* `imo.imo1959_q1`
* `imo.imo1960_q1`
* `imo.imo1962_q1`
* `imo.imo1962_q4`
* `imo.imo1964_q1`
* `imo.imo1969_q1`
* `imo.imo1972_q5`
* `imo.imo1975_q1`
* `imo.imo1977_q6`
* `imo.imo1981_q3`
* `imo.imo1987_q1`
* `imo.imo1988_q6`
* `imo.imo1994_q1`
* `imo.imo1998_q2`
* `imo.imo2001_q2`
* `imo.imo2001_q6`
* `imo.imo2005_q3`
* `imo.imo2005_q4`
* `imo.imo2006_q3`
* `imo.imo2006_q5`
* `imo.imo2008_q2`
* `imo.imo2008_q3`
* `imo.imo2008_q4`
* `imo.imo2011_q3`
* `imo.imo2011_q5`
* `imo.imo2013_q1`
* `imo.imo2013_q5`
* `imo.imo2019_q1`
* `imo.imo2019_q2`
* `imo.imo2019_q4`
* `imo.imo2020_q2`
* `imo.imo2021_q1`
* `linear_order_with_pos_mul_pos_eq_zero`
* `map_floor`
* `miu_language.basic`
* `miu_language.decision_nec`
* `miu_language.decision_suf`
* `oxford_invariants.2021summer.week3_p1`
* `phillips`
* `pseudoelement`
* `quadratic_form`
* `seminorm_lattice_not_distrib`
* `sensitivity`
* `sorgenfrey_line`
* `wiedijk_100_theorems.abel_ruffini`
* `wiedijk_100_theorems.area_of_a_circle`
* `wiedijk_100_theorems.ascending_descending_sequences`
* `wiedijk_100_theorems.ballot_problem`
* `wiedijk_100_theorems.birthday_problem`
* `wiedijk_100_theorems.cubing_a_cube`
* `wiedijk_100_theorems.friendship_graphs`
* `wiedijk_100_theorems.herons_formula`
* `wiedijk_100_theorems.inverse_triangle_sum`
* `wiedijk_100_theorems.konigsberg`
* `wiedijk_100_theorems.partition`
* `wiedijk_100_theorems.perfect_numbers`
* `wiedijk_100_theorems.solution_of_cubic`
* `wiedijk_100_theorems.sum_of_prime_reciprocals_diverges`
* `zero_divisors_in_add_monoid_algebras`

Author: leanprover-community-bot

archive/arithcc.lean

@@ -9,6 +9,9 @@ import tactic.basic
 /-!
 # A compiler for arithmetic expressions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A formalization of the correctness of a compiler from arithmetic expressions to machine language
 described by McCarthy and Painter, which is considered the first proof of compiler correctness.
 

archive/examples/mersenne_primes.lean

@@ -8,6 +8,9 @@ import number_theory.lucas_lehmer
 /-!
 # Explicit Mersenne primes
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We run some Lucas-Lehmer tests to prove some Mersenne primes are prime.
 
 See the discussion at the end of [src/number_theory/lucas_lehmer.lean]

archive/examples/prop_encodable.lean

@@ -9,6 +9,9 @@ import data.W.basic
 /-!
 # W types
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The file `data/W.lean` shows that if `α` is an an encodable fintype and for every `a : α`,
 `β a` is encodable, then `W β` is encodable.
 

archive/imo/imo1959_q1.lean

@@ -10,6 +10,9 @@ import data.nat.prime
 /-!
 # IMO 1959 Q1
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Prove that the fraction `(21n+4)/(14n+3)` is irreducible for every natural number `n`.
 
 Since Lean doesn't have a concept of "irreducible fractions" per se, we just formalize this

archive/imo/imo1960_q1.lean

@@ -9,6 +9,9 @@ import data.nat.digits
 /-!
 # IMO 1960 Q1
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Determine all three-digit numbers $N$ having the property that $N$ is divisible by 11, and
 $\dfrac{N}{11}$ is equal to the sum of the squares of the digits of $N$.
 

archive/imo/imo1962_q1.lean

@@ -9,6 +9,9 @@ import data.nat.digits
 /-!
 # IMO 1962 Q1
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Find the smallest natural number $n$ which has the following properties:
 
 (a) Its decimal representation has 6 as the last digit.

archive/imo/imo1962_q4.lean

@@ -9,6 +9,9 @@ import analysis.special_functions.trigonometric.complex
 /-!
 # IMO 1962 Q4
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Solve the equation `cos x ^ 2 + cos (2 * x) ^ 2 + cos (3 * x) ^ 2 = 1`.
 
 Since Lean does not have a concept of "simplest form", we just express what is

archive/imo/imo1964_q1.lean

@@ -10,6 +10,9 @@ import data.nat.modeq
 /-!
 # IMO 1964 Q1
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 (a) Find all positive integers $n$ for which $2^n-1$ is divisible by $7$.
 
 (b) Prove that there is no positive integer $n$ for which $2^n+1$ is divisible by $7$.

archive/imo/imo1969_q1.lean

@@ -11,6 +11,9 @@ import data.set.finite
 /-!
 # IMO 1969 Q1
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Prove that there are infinitely many natural numbers $a$ with the following property:
 the number $z = n^4 + a$ is not prime for any natural number $n$.
 -/

archive/imo/imo1972_q5.lean

@@ -10,6 +10,9 @@ import analysis.normed_space.basic
 /-!
 # IMO 1972 Q5
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Problem: `f` and `g` are real-valued functions defined on the real line. For all `x` and `y`,
 `f(x + y) + f(x - y) = 2f(x)g(y)`. `f` is not identically zero and `|f(x)| ≤ 1` for all `x`.
 Prove that `|g(x)| ≤ 1` for all `x`.