Mathlib v4.30 source proposition Int.even_add'

Identifier: F:ml430-int-even-add-bc8e1394
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

The proposition declared as `Int.even_add'` in the pinned Mathlib v4.30 source.

Formal statement

∀ {m n : ℤ}, Even (m + n) ↔ (Odd m ↔ Odd n)

Dependencies

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7 direct dependencies 0 direct dependents

Evidence

kernel-Int.even_add_prime

Kind: kernel-term
Status: checked

Supports: The proposition declared as `Int.even_add'` in the pinned Mathlib v4.30 source.

Checker command

cargo test -p axeyum-lean-kernel --lib int_prelude::

Evidence notes

`Int.even_add'` in `crates/axeyum-lean-kernel/src/int_prelude/parity.rs` (`declare_even_add_prime`, kernel name `even_add'` via the same apostrophe-suffix convention as `Nat.bitwise_bit'`). Confirmed a DIFFERENT proposition from `F:ml430-int-even-add-3c4536e3` (`Int.even_add`) by reading both Mathlib source files directly (`Mathlib/Algebra/Group/Int/Even.lean` for `even_add`, `Mathlib/Algebra/Ring/Int/Parity.lean` for `even_add'`), per the prior lane's finding. Shares `declare_even_add`'s outer case-split and additive-`emod` machinery (`even_add_family_stmt_and_proof`, `modeq_add`); the only difference is the inner predicate (`Odd` via `odd_fact`/`odd_pred` instead of `Even` via `even_fact`/`even_pred`).

footprint-Int.even_add_prime

Kind: exhaustive-enumeration
Status: checked

Supports: axiom_footprint: [] -- this theorem's trusted closure is empty

Checker command

test "$(cargo run --release -q -p axeyum-lean-kernel --example theorem_axiom_footprint -- Int.even_add 2>/dev/null | /usr/bin/grep -xFc $'integer\tInt.even_add\'\t0\t')" -ge 1

Evidence notes

The matched row is `integer<TAB>Int.even_add'<TAB>0<TAB>` with an EMPTY trailing footprint column, so a nonzero footprint or an absent declaration both give a count of 0 and fail. Uses `/usr/bin/grep` explicitly (not the interactive `ugrep` alias) and ANSI-C-quoted literal tabs; the `-xF` exact-line grep matters here because the CLI's own name-argument filter is a prefix match (`Int.even_add` alone also returns this row and `Int.even_add_one`'s). Verified to pass for real (count 1) and to fail on a mutated footprint (`...\t1\t`, count 0) and a nonexistent name (count 0). Run `--release`: in debug, building the full constructed environment stack-overflows, which is a resource limit and not a fact about this theorem.

Provenance

{
  "date": "2026-08-29",
  "established_by": "not established in this ledger",
  "source": "statement-only extraction of `Int.even_add'` from Mathlib v4.30.0; no proof value was exposed",
  "prior_art": [
    {
      "who": "the Mathlib contributors",
      "what": "the theorem declaration `Int.even_add'`",
      "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"
    }
  ]
}