DEFINITION and4_ind()
TYPE =
       ∀P0:Prop
         .∀P1:Prop.∀P2:Prop.∀P3:Prop.∀P:Prop.(P0→P1→P2→P3→P)→(and4 P0 P1 P2 P3)→P
BODY =
        assume P0: Prop
        assume P1: Prop
        assume P2: Prop
        assume P3: Prop
        assume P: Prop
        suppose H: P0→P1→P2→P3→P
        suppose H1: and4 P0 P1 P2 P3
          by cases on H1 we prove P
             case and4_intro H2:P0 H3:P1 H4:P2 H5:P3 ⇒
                the thesis becomes P
                by (H H2 H3 H4 H5)
P
          we proved P
       we proved 
          ∀P0:Prop
            .∀P1:Prop.∀P2:Prop.∀P3:Prop.∀P:Prop.(P0→P1→P2→P3→P)→(and4 P0 P1 P2 P3)→P