let R be Ring; :: thesis: for c being Data-Location of R

for i1 being Nat

for s being State of (SCM R) holds

( (Exec ((goto (i1,R)),s)) . (IC ) = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

let c be Data-Location of R; :: thesis: for i1 being Nat

for s being State of (SCM R) holds

( (Exec ((goto (i1,R)),s)) . (IC ) = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

let i1 be Nat; :: thesis: for s being State of (SCM R) holds

( (Exec ((goto (i1,R)),s)) . (IC ) = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

let s be State of (SCM R); :: thesis: ( (Exec ((goto (i1,R)),s)) . (IC ) = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

A1: the_Values_of (SCM R) = (SCM-VAL R) * SCM-OK by Lm1;

reconsider S = s as SCM-State of R by A1, CARD_3:107;

reconsider i = 6 as Element of Segm 8 by NAT_1:44;

reconsider I = goto (i1,R) as Element of SCM-Instr R by Def1;

I = [i,<*i1*>,{}] ;

then A2: I jump_address = i1 by SCMRINGI:2;

A3: i1 in NAT by ORDINAL1:def 12;

A4: Exec ((goto (i1,R)),s) = SCM-Exec-Res (I,S) by Th10

.= SCM-Chg (S,(I jump_address)) by SCMRING1:def 14, A3 ;

thus (Exec ((goto (i1,R)),s)) . (IC ) = (Exec ((goto (i1,R)),s)) . NAT by Def1

.= i1 by A4, A2, SCMRING1:7 ; :: thesis: (Exec ((goto (i1,R)),s)) . c = s . c

c is Element of Data-Locations by Th1;

hence (Exec ((goto (i1,R)),s)) . c = s . c by A4, AMI_3:27, SCMRING1:8; :: thesis: verum

for i1 being Nat

for s being State of (SCM R) holds

( (Exec ((goto (i1,R)),s)) . (IC ) = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

let c be Data-Location of R; :: thesis: for i1 being Nat

for s being State of (SCM R) holds

( (Exec ((goto (i1,R)),s)) . (IC ) = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

let i1 be Nat; :: thesis: for s being State of (SCM R) holds

( (Exec ((goto (i1,R)),s)) . (IC ) = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

let s be State of (SCM R); :: thesis: ( (Exec ((goto (i1,R)),s)) . (IC ) = i1 & (Exec ((goto (i1,R)),s)) . c = s . c )

A1: the_Values_of (SCM R) = (SCM-VAL R) * SCM-OK by Lm1;

reconsider S = s as SCM-State of R by A1, CARD_3:107;

reconsider i = 6 as Element of Segm 8 by NAT_1:44;

reconsider I = goto (i1,R) as Element of SCM-Instr R by Def1;

I = [i,<*i1*>,{}] ;

then A2: I jump_address = i1 by SCMRINGI:2;

A3: i1 in NAT by ORDINAL1:def 12;

A4: Exec ((goto (i1,R)),s) = SCM-Exec-Res (I,S) by Th10

.= SCM-Chg (S,(I jump_address)) by SCMRING1:def 14, A3 ;

thus (Exec ((goto (i1,R)),s)) . (IC ) = (Exec ((goto (i1,R)),s)) . NAT by Def1

.= i1 by A4, A2, SCMRING1:7 ; :: thesis: (Exec ((goto (i1,R)),s)) . c = s . c

c is Element of Data-Locations by Th1;

hence (Exec ((goto (i1,R)),s)) . c = s . c by A4, AMI_3:27, SCMRING1:8; :: thesis: verum