proofGearsTermS : {c10 :  !$\mathbb{N}$! } !$\rightarrow$! !$\top$!
proofGearsTermS {c10} = whileTest!$\prime$! {_} {_}  {c10} (!$\lambda$! n p !$\rightarrow$!  conversion1 n p (!$\lambda$! n1 p1 !$\rightarrow$!
    TerminatingLoopS Env (!$\lambda$! env !$\rightarrow$! varn env)
        (!$\lambda$! n2 p2 loop !$\rightarrow$! whileLoopSeg {_} {_} {c10} n2 p2 loop (!$\lambda$! ne pe !$\rightarrow$! whileTestSpec1 c10 ne pe)) n1 p1 ))