loopPPSem : (input output : Envc ) !$\rightarrow$!  output !$\equiv$! loopPP (varn input)  input refl
  !$\rightarrow$! (varn input + vari input !$\equiv$! c10 input ) 
  !$\rightarrow$! (varn input + vari input !$\equiv$! c10 input ) implies (vari output !$\equiv$! c10 output)
loopPPSem input output refl s2p = loopPPSemInduct (varn input) input  refl refl s2p