| {"problem_id": "triv_add_zero", "source": "trivial", "split": "dev", "area": "algebra", "difficulty": 1, "informal_statement": "For every natural number n, n + 0 = n.", "formal_statement": "theorem triv_add_zero (n : ℕ) : n + 0 = n := by sorry"} | |
| {"problem_id": "triv_add_comm", "source": "trivial", "split": "dev", "area": "algebra", "difficulty": 1, "informal_statement": "Addition of natural numbers is commutative: a + b = b + a.", "formal_statement": "theorem triv_add_comm (a b : ℕ) : a + b = b + a := by sorry"} | |
| {"problem_id": "triv_square_expand", "source": "trivial", "split": "dev", "area": "algebra", "difficulty": 1, "informal_statement": "For all integers a and b, (a + b)^2 = a^2 + 2ab + b^2.", "formal_statement": "theorem triv_square_expand (a b : ℤ) : (a + b) ^ 2 = a ^ 2 + 2 * a * b + b ^ 2 := by sorry"} | |
| {"problem_id": "triv_even_square", "source": "trivial", "split": "dev", "area": "number_theory", "difficulty": 1, "informal_statement": "If n is an even natural number then n^2 is even.", "formal_statement": "theorem triv_even_square (n : ℕ) (h : Even n) : Even (n ^ 2) := by sorry"} | |
| {"problem_id": "triv_dvd_trans", "source": "trivial", "split": "dev", "area": "number_theory", "difficulty": 1, "informal_statement": "Divisibility of integers is transitive: if a divides b and b divides c then a divides c.", "formal_statement": "theorem triv_dvd_trans (a b c : ℤ) (h1 : a ∣ b) (h2 : b ∣ c) : a ∣ c := by sorry"} | |