let f be INT-Exec ; :: thesis: for v being INT-Variable of NAT

for t being INT-Expression of NAT holds v,t form_assignment_wrt f

set S = ECIW-signature ;

set G = INT-ElemIns ;

set X = NAT ;

set A = FreeUnivAlgNSG (ECIW-signature,INT-ElemIns);

let v be INT-Variable of NAT; :: thesis: for t being INT-Expression of NAT holds v,t form_assignment_wrt f

let t be INT-Expression of NAT; :: thesis: v,t form_assignment_wrt f

reconsider v9 = v as Element of Funcs ((Funcs (NAT,INT)),NAT) by FUNCT_2:8;

reconsider t9 = t as Element of Funcs ((Funcs (NAT,INT)),INT) by FUNCT_2:8;

A1: Terminals (DTConUA (ECIW-signature,INT-ElemIns)) = INT-ElemIns by FREEALG:3;

A2: [v9,t9] in INT-ElemIns by ZFMISC_1:87;

A3: ElementaryInstructions (FreeUnivAlgNSG (ECIW-signature,INT-ElemIns)) = FreeGenSetNSG (ECIW-signature,INT-ElemIns) by AOFA_000:70;

then root-tree [v9,t9] in ElementaryInstructions (FreeUnivAlgNSG (ECIW-signature,INT-ElemIns)) by A1, A2;

then reconsider I = root-tree [v9,t9] as Element of (FreeUnivAlgNSG (ECIW-signature,INT-ElemIns)) ;

take I ; :: according to AOFA_I00:def 15 :: thesis: ( I in ElementaryInstructions (FreeUnivAlgNSG (ECIW-signature,INT-ElemIns)) & ( for s being Element of Funcs (NAT,INT) holds f . (s,I) = s +* ((v . s),(t . s)) ) )

thus I in ElementaryInstructions (FreeUnivAlgNSG (ECIW-signature,INT-ElemIns)) by A3, A1, A2; :: thesis: for s being Element of Funcs (NAT,INT) holds f . (s,I) = s +* ((v . s),(t . s))

thus for s being Element of Funcs (NAT,INT) holds f . (s,I) = s +* ((v . s),(t . s)) by Def25; :: thesis: verum

for t being INT-Expression of NAT holds v,t form_assignment_wrt f

set S = ECIW-signature ;

set G = INT-ElemIns ;

set X = NAT ;

set A = FreeUnivAlgNSG (ECIW-signature,INT-ElemIns);

let v be INT-Variable of NAT; :: thesis: for t being INT-Expression of NAT holds v,t form_assignment_wrt f

let t be INT-Expression of NAT; :: thesis: v,t form_assignment_wrt f

reconsider v9 = v as Element of Funcs ((Funcs (NAT,INT)),NAT) by FUNCT_2:8;

reconsider t9 = t as Element of Funcs ((Funcs (NAT,INT)),INT) by FUNCT_2:8;

A1: Terminals (DTConUA (ECIW-signature,INT-ElemIns)) = INT-ElemIns by FREEALG:3;

A2: [v9,t9] in INT-ElemIns by ZFMISC_1:87;

A3: ElementaryInstructions (FreeUnivAlgNSG (ECIW-signature,INT-ElemIns)) = FreeGenSetNSG (ECIW-signature,INT-ElemIns) by AOFA_000:70;

then root-tree [v9,t9] in ElementaryInstructions (FreeUnivAlgNSG (ECIW-signature,INT-ElemIns)) by A1, A2;

then reconsider I = root-tree [v9,t9] as Element of (FreeUnivAlgNSG (ECIW-signature,INT-ElemIns)) ;

take I ; :: according to AOFA_I00:def 15 :: thesis: ( I in ElementaryInstructions (FreeUnivAlgNSG (ECIW-signature,INT-ElemIns)) & ( for s being Element of Funcs (NAT,INT) holds f . (s,I) = s +* ((v . s),(t . s)) ) )

thus I in ElementaryInstructions (FreeUnivAlgNSG (ECIW-signature,INT-ElemIns)) by A3, A1, A2; :: thesis: for s being Element of Funcs (NAT,INT) holds f . (s,I) = s +* ((v . s),(t . s))

thus for s being Element of Funcs (NAT,INT) holds f . (s,I) = s +* ((v . s),(t . s)) by Def25; :: thesis: verum