Addition on the constructed reals is right-cancellative

Identifier: F:creal-add-right-cancel
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

For constructed reals x0, x1 and x2, if x0 + x2 is CReal.Equiv-equivalent to x1 + x2, then x0 is CReal.Equiv-equivalent to x1.

Formal statement

theorem CReal.add_right_cancel : ((x0 : CReal) -> ((x1 : CReal) -> ((x2 : CReal) -> ((x3 : CReal.Equiv (CReal.add x0 x2) (CReal.add x1 x2)) -> CReal.Equiv x0 x1))))

Dependencies

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

7 direct dependencies 35 direct dependents Graph shows the first 8 on each side.

Evidence

kernel-CReal.add_right_cancel

Kind: kernel-term
Status: checked

Supports: CReal.add_right_cancel is admitted by the trusted kernel gate with the type recorded in formal.statement.

Checker command

cargo run -q --release -p axeyum-lean-kernel --example theorem_dependency_inventory -- CReal.add_right_cancel 2>/dev/null | grep -cE '^CReal\.add_right_cancel[[:space:]]'

Evidence notes

`build_creal_prelude`/`build_cpoint_prelude` admits this theorem through the trusted `Kernel::add_declaration` gate, which re-checks the proof term against the stated type, so a line in this tool's output for the exact name is a machine-checked proof having been admitted. `theorem_dependency_inventory` builds creal/complex/cpoint in one run; it exits non-zero for a named filter that matches nothing, and `grep -c` (never `-q`) independently asserts the exact tab-anchored line is present. `--release` is MANDATORY: building the constructed carriers recurses deep enough in a debug build to overflow the default thread stack (measured on this tree: release exits 0, debug SIGABRTs at 134).

footprint-CReal.add_right_cancel

Kind: exhaustive-enumeration
Status: checked

Supports: axiom_footprint: [] -- the cpoint prelude's trusted surface is empty, which bounds CReal.add_right_cancel

Checker command

cargo run -q --release -p axeyum-lean-kernel --example nat_axiom_inventory -- --include-constructed --require-axiom-free cpoint

Evidence notes

`nat_axiom_inventory --include-constructed --require-axiom-free cpoint` builds the cpoint environment as its own group and reports `cpoint: axiom=0 opaque=0 quotient=0 total_trusted=0` (re-measured on this tree), covering Axiom, Opaque AND Quotient, not just Declaration::Axiom. This bounds every individual cpoint theorem's footprint by []. `--include-constructed` is REQUIRED here -- verified: without it the command exits 1 with "\"cpoint\" is a known prelude but was NOT built this run ... need --include-constructed", rather than a silent pass; this is the standing trap of an empty/absent result reading as a strong negative when the tool was never pointed at the subject. `--release` is ALSO load-bearing here, and this is a bug this batch found in the pre-existing F-creal-add-comm.json-style pattern (which omits it): measured on this tree, `cargo run -q -p axeyum-lean-kernel --example nat_axiom_inventory -- --include-constructed --require-axiom-free creal` (no --release) SIGABRTs with 'has overflowed its stack', exit 134 -- the same deep-recursion resource limit already documented for prelude_theorem_inventory and theorem_dependency_inventory, just not previously measured for this tool. `--release` fixes it: exit 0.

Provenance

{
  "date": "2026-08-25",
  "established_by": "axeyum-lean-kernel build_cpoint_prelude",
  "source": "theorem name and dependency edges from theorem_dependency_inventory; canonical type read via a standalone probe binary depending on axeyum-lean-kernel by path, calling only its public Kernel API (environment(), display_name(), render_lean(), axiom_footprint()) -- crates/ source untouched."
}