let a, b, c be Int-Location ; :: thesis: ( a <> b & a <> c implies Divide b,c does_not_destroy a )
assume A1: ( a <> b & a <> c ) ; :: thesis: Divide b,c does_not_destroy a

now

let e be Int-Location ; :: thesis: for l being Element of NAT
for h being FinSeq-Location holds
( a := e <> Divide b,c & AddTo a,e <> Divide b,c & SubFrom a,e <> Divide b,c & MultBy a,e <> Divide b,c & Divide e,a <> Divide b,c & Divide a,e <> Divide b,c & a := h,e <> Divide b,c & a :=len h <> Divide b,c )
let l be Element of NAT ; :: thesis: for h being FinSeq-Location holds
( a := e <> Divide b,c & AddTo a,e <> Divide b,c & SubFrom a,e <> Divide b,c & MultBy a,e <> Divide b,c & Divide e,a <> Divide b,c & Divide a,e <> Divide b,c & a := h,e <> Divide b,c & a :=len h <> Divide b,c )
let h be FinSeq-Location ; :: thesis: ( a := e <> Divide b,c & AddTo a,e <> Divide b,c & SubFrom a,e <> Divide b,c & MultBy a,e <> Divide b,c & Divide e,a <> Divide b,c & Divide a,e <> Divide b,c & a := h,e <> Divide b,c & a :=len h <> Divide b,c )
A2: InsCode (Divide b,c) = 5 by SCMFSA_2:46;
hence a := e <> Divide b,c by SCMFSA_2:42; :: thesis: ( AddTo a,e <> Divide b,c & SubFrom a,e <> Divide b,c & MultBy a,e <> Divide b,c & Divide e,a <> Divide b,c & Divide a,e <> Divide b,c & a := h,e <> Divide b,c & a :=len h <> Divide b,c )
thus AddTo a,e <> Divide b,c by A2, SCMFSA_2:43; :: thesis: ( SubFrom a,e <> Divide b,c & MultBy a,e <> Divide b,c & Divide e,a <> Divide b,c & Divide a,e <> Divide b,c & a := h,e <> Divide b,c & a :=len h <> Divide b,c )
thus SubFrom a,e <> Divide b,c by A2, SCMFSA_2:44; :: thesis: ( MultBy a,e <> Divide b,c & Divide e,a <> Divide b,c & Divide a,e <> Divide b,c & a := h,e <> Divide b,c & a :=len h <> Divide b,c )
thus MultBy a,e <> Divide b,c by A2, SCMFSA_2:45; :: thesis: ( Divide e,a <> Divide b,c & Divide a,e <> Divide b,c & a := h,e <> Divide b,c & a :=len h <> Divide b,c )
thus ( Divide e,a <> Divide b,c & Divide a,e <> Divide b,c ) by A1, SF_MASTR:9; :: thesis: ( a := h,e <> Divide b,c & a :=len h <> Divide b,c )
thus a := h,e <> Divide b,c by A2, SCMFSA_2:50; :: thesis: a :=len h <> Divide b,c
thus a :=len h <> Divide b,c by A2, SCMFSA_2:52; :: thesis: verum

end;

hence Divide b,c does_not_destroy a by Def3; :: thesis: verum