Summary: Stokes' Theorem.
Let n be a positive integer, let V be an open subset of Rn
and let m be an integer such that 1 m n.
Stokes' Theorem will follow rather directly from the definition of the integral of a differential form over
a submanifold and the following Proposition.
Proposition. Suppose Am-1
d(t)(e1, . . . , em) dt = 0
d(t)(e1, . . . , em) dt = (-1)m
(s)(e1, . . . , em-1) ds.
Proof. For each j = 1, . . . , m set fj = ej