Mathlib v4.30 source proposition Int.even_add_one

Identifier: F:ml430-int-even-add-one-af33da18
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

∀ {n : ℤ}, Even (n + 1) ↔ ¬Even n

Dependencies

The graph shows direct ledger edges. Follow a node to open its artifact page.

8 direct dependencies 0 direct dependents

Evidence

kernel-Int.even_add_one

Kind: kernel-term
Status: checked

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

Checker command

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

Evidence notes

`Int.even_add_one` in `crates/axeyum-lean-kernel/src/int_prelude/parity.rs` (`declare_even_add_one`). Mirrors Mathlib v4.30's `Int.even_add_one` verbatim. A two-case (not four-case) specialisation of the same additive-`emod` machinery as `Int.even_add`/`Int.even_add'`: `add_one_parity_hyp` computes `(n+1)`'s residue via `modeq_add` with the second addend's `ModEq` fixed to `Int.mod_eq_refl` (since `ModEq 2 one one` needs no case split), then reads the parity back off via `emod_zero_implies_even`/`emod_one_implies_odd`.

footprint-Int.even_add_one

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_one 2>/dev/null | /usr/bin/grep -xFc $'integer\tInt.even_add_one\t0\t')" -ge 1

Evidence notes

The matched row is `integer<TAB>Int.even_add_one<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. Verified to pass for real (count 1) and to fail on a mutated footprint (`...\t1\t`, count 0) and a nonexistent name (`Int.even_add_one_bogus`, 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_one` from Mathlib v4.30.0; no proof value was exposed",
  "prior_art": [
    {
      "who": "the Mathlib contributors",
      "what": "the theorem declaration `Int.even_add_one`",
      "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"
    }
  ]
}