A.3.1:5.3 - Proof or derivation

Gauss_Elimination applies to a matrix and right-hand side over a declared algebraic domain in which the required row operations and pivots are valid. A mathematician or proof system enacting it applies equivalence-preserving row operations until solved or echelon form is reached. A missing admissible pivot, unsupported division, or unspecified domain is a stop. The visible result here is a method identification that a later derivation may enact.

Recover the claim-bearing episteme expressed by a textbook explanation, proof-assistant script, or formal rule set; apply A.3.2’s membership test for Gauss_Elimination. A concrete proof-assistant run is Work, and the algebraic structure may be a formal substrate. Using the resulting proof for a project decision additionally needs an evidence or assurance relation.