Metamath Proof Explorer

Theorem mzpconstmpt

Description: A constant function expressed in maps-to notation is polynomial. This theorem and the several that follow ( mzpaddmpt , mzpmulmpt , mzpnegmpt , mzpsubmpt , mzpexpmpt ) can be used to build proofs that functions which are "manifestly polynomial", in the sense of being a maps-to containing constants, projections, and simple arithmetic operations, are actually polynomial functions. There is no mzpprojmpt because mzpproj is already expressed using maps-to notation. (Contributed by Stefan O'Rear, 5-Oct-2014)

Ref Expression
Assertion mzpconstmpt V V C x V C mzPoly V


Step Hyp Ref Expression
1 fconstmpt V × C = x V C
2 mzpconst V V C V × C mzPoly V
3 1 2 eqeltrrid V V C x V C mzPoly V