Artifact · proved
This page records one proposition and the evidence attached to it. Text from the source ledger is shown as record data.
Recorded description
The proposition declared as `Nat.Prime.dvd_mul` in the pinned Mathlib v4.30 source.
∀ {p m n : ℕ}, Nat.Prime p → (p ∣ m * n ↔ p ∣ m ∨ p ∣ n)The graph shows direct ledger edges. Follow a node to open its artifact page.
Supports: ∀ {p m n : ℕ}, Nat.Prime p → (p ∣ m * n ↔ p ∣ m ∨ p ∣ n)
test "$(cargo run -q -p axeyum-lean-kernel --example nat_theorem_inventory -- prime_dvd_mul_iff 2>/dev/null | grep -Ec '^Nat\.prime_dvd_mul_iff[[:space:]]')" -ge 1`mp` is `euclid_lemma` (`bezout.rs`) applied and partially saturated at the hypothesis slot. `mpr` case-splits the `Or` via `dvd_mul_right_of_dvd`/`dvd_mul_left_of_dvd`.
Supports: axiom_footprint: [] -- the Nat prelude's trusted surface is empty
cargo run -q -p axeyum-lean-kernel --example nat_axiom_inventory -- --require-axiom-free nat`nat_axiom_inventory --require-axiom-free nat` enumerates the built Nat environment and exits non-zero unless it admits no Axiom, Opaque or Quotient declaration. A theorem cannot depend on a trusted declaration the environment does not contain, so an empty trusted surface bounds `Nat.prime_dvd_mul_iff`'s footprint by [].
{
"date": "2026-08-30",
"established_by": "axeyum-lean-kernel build_nat_prelude, lane prime-dvd-mirrors",
"source": "statement-only extraction of `Nat.Prime.dvd_mul` from Mathlib v4.30.0; no proof value was exposed",
"prior_art": [
{
"who": "the Mathlib contributors",
"what": "the theorem declaration `Nat.Prime.dvd_mul`",
"where": "mathlib4 commit c5ea00351c28e24afc9f0f84379aa41082b1188f (v4.30.0)",
"year": 2026,
"attribution": "the proposition was read from the pinned statement-only inventory; the proof term and tactic trace were not consulted"
}
]
}