An abstract nonlinear Cauchy-Kovalevska theorem

Inhomogeneous Two-Parameter Abstract Cauchy Problem

An abstract standardisation theorem

The standardisation theorem is a key theorem in the-calculus. It implies that any normal form can be reached by the normal order (leftmost outermost) strategy. The theorem states that any reduction may be rearranged in a top-down and left-to-right order. This also holds in orthogonal term rewriting systems (TRS), although the left-to-right order is more subtle. We give a new presentation of the...

Cauchy Integral Theorem

where we use the notation dxI for (1.4) dxI = dxi1 ∧ dxi2 ∧ ... ∧ dxik for I = {i1, i2, ..., ik} with i1 < i2 < ... < ik. So ΩX is a free module over C ∞(X) generated by dxI . Obviously, Ω k X = 0 for k > n and ⊕ΩX is a graded ring (noncommutative without multiplicative identity) with multiplication defined by the wedge product (1.5) ∧ : (ω1, ω2)→ ω1 ∧ ω2. Note that (1.6) ω1 ∧ ω2 = (−1)12ω2 ∧ ω...

Cauchy Mean Theorem

The purpose of this paper was to prove formally, using the Mizar language, Arithmetic Mean/Geometric Mean theorem known maybe better under the name of AM-GM inequality or Cauchy mean theorem. It states that the arithmetic mean of a list of a non-negative real numbers is greater than or equal to the geometric mean of the same list. The formalization was tempting for at least two reasons: one of ...

inhomogeneous two-parameter abstract cauchy problem