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

now

let e be Int-Location ; :: thesis: for l being Element of NAT
for f being FinSeq-Location holds
( a := e <> AddTo b,c & AddTo a,e <> AddTo b,c & SubFrom a,e <> AddTo b,c & MultBy a,e <> AddTo b,c & Divide a,e <> AddTo b,c & Divide e,a <> AddTo b,c & a := f,e <> AddTo b,c & a :=len f <> AddTo b,c )
let l be Element of NAT ; :: thesis: for f being FinSeq-Location holds
( a := e <> AddTo b,c & AddTo a,e <> AddTo b,c & SubFrom a,e <> AddTo b,c & MultBy a,e <> AddTo b,c & Divide a,e <> AddTo b,c & Divide e,a <> AddTo b,c & a := f,e <> AddTo b,c & a :=len f <> AddTo b,c )
let f be FinSeq-Location ; :: thesis: ( a := e <> AddTo b,c & AddTo a,e <> AddTo b,c & SubFrom a,e <> AddTo b,c & MultBy a,e <> AddTo b,c & Divide a,e <> AddTo b,c & Divide e,a <> AddTo b,c & a := f,e <> AddTo b,c & a :=len f <> AddTo b,c )
A2: InsCode (AddTo b,c) = 2 by SCMFSA_2:43;
hence a := e <> AddTo b,c by SCMFSA_2:42; :: thesis: ( AddTo a,e <> AddTo b,c & SubFrom a,e <> AddTo b,c & MultBy a,e <> AddTo b,c & Divide a,e <> AddTo b,c & Divide e,a <> AddTo b,c & a := f,e <> AddTo b,c & a :=len f <> AddTo b,c )
thus AddTo a,e <> AddTo b,c by A1, SF_MASTR:6; :: thesis: ( SubFrom a,e <> AddTo b,c & MultBy a,e <> AddTo b,c & Divide a,e <> AddTo b,c & Divide e,a <> AddTo b,c & a := f,e <> AddTo b,c & a :=len f <> AddTo b,c )
thus SubFrom a,e <> AddTo b,c by A2, SCMFSA_2:44; :: thesis: ( MultBy a,e <> AddTo b,c & Divide a,e <> AddTo b,c & Divide e,a <> AddTo b,c & a := f,e <> AddTo b,c & a :=len f <> AddTo b,c )
thus MultBy a,e <> AddTo b,c by A2, SCMFSA_2:45; :: thesis: ( Divide a,e <> AddTo b,c & Divide e,a <> AddTo b,c & a := f,e <> AddTo b,c & a :=len f <> AddTo b,c )
thus ( Divide a,e <> AddTo b,c & Divide e,a <> AddTo b,c ) by A2, SCMFSA_2:46; :: thesis: ( a := f,e <> AddTo b,c & a :=len f <> AddTo b,c )
thus a := f,e <> AddTo b,c by A2, SCMFSA_2:50; :: thesis: a :=len f <> AddTo b,c
thus a :=len f <> AddTo b,c by A2, SCMFSA_2:52; :: thesis: verum

end;

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