PD0022 · conservative definition

BoundedQRes

a has a square root strictly below m modulo m.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Readable signature

BoundedQRes(m, a)

Exact expansion

exists qr_x_defined_bounded_qres. (exists qr_h_defined_bounded_qres. qr_h_defined_bounded_qres + S qr_x_defined_bounded_qres = m) /\ exists qr_u_defined_bounded_qres qr_v_defined_bounded_qres. qr_x_defined_bounded_qres * qr_x_defined_bounded_qres + m * qr_u_defined_bounded_qres = a + m * qr_v_defined_bounded_qres

This node is conservative notation, not a theorem, axiom, predicate constant, or kernel rule. Its expansion remains in the unchanged first-order language.

Definition neighborhood

Depends on conservative definitions

Used by conservative definitions

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All transitive conservative prerequisites

Used by theorem statements or local proof propositions

Grand-campaign planning vocabulary

Locate BoundedQRes in the global campaign vocabulary →

Reviewed BoundedQRes corresponds to blueprint BoundedQRes with checked argument positions [0, 1].

The global atlas describes planning vocabulary and does not itself certify a definition or theorem. The reviewed expansion and conservative dependency DAG on this page are the actual family-local reading definitions.