let K be non empty left_unital doubleLoopStr ; :: thesis: for V, W being non empty VectSpStr of K
for f being Form of V,W holds (1. K) * f = f
let V, W be non empty VectSpStr of K; :: thesis: for f being Form of V,W holds (1. K) * f = f
let f be Form of V,W; :: thesis: (1. K) * f = f

now

let v be Vector of V; :: thesis: for w being Vector of W holds ((1. K) * f) . v,w = f . v,w
let w be Vector of W; :: thesis: ((1. K) * f) . v,w = f . v,w
thus ((1. K) * f) . v,w = (1. K) * (f . v,w) by Def4
.= f . v,w by VECTSP_1:def 19 ; :: thesis: verum

end;

hence (1. K) * f = f by BINOP_1:2; :: thesis: verum