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Step * 1 1 of Lemma int_term_value_subtract_lemma


1. y : Top@i
2. x : Top@i
3. f : Top@i
⊢ int_term_ind(x;
               itermConstant(const)⇒ const;
               itermVar(var)⇒ f var;
               itermAdd(left,right)⇒ rec1,rec2.rec1 + rec2;
               itermSubtract(left,right)⇒ rec3,rec4.rec3 - rec4;
               itermMultiply(left,right)⇒ rec5,rec6.rec5 * rec6;
               itermMinus(num)⇒ rec7.-rec7)  - int_term_ind(y;
                                                             itermConstant(const)⇒ const;
                                                             itermVar(var)⇒ f var;
                                                             itermAdd(left,right)⇒ rec1,rec2.rec1 + rec2;
                                                             itermSubtract(left,right)⇒ rec3,rec4.rec3 - rec4;
                                                             itermMultiply(left,right)⇒ rec5,rec6.rec5 * rec6;
                                                             itermMinus(num)⇒ rec7.-rec7)  ~ int_term_value(f;x) 
- int_term_value(f;y)
BY
{ Try (RW (AddrC [2] (UnfoldC `int_term_value`)) 0)⋅ }

1
1. y : Top@i
2. x : Top@i
3. f : Top@i
⊢ int_term_ind(x;
               itermConstant(const)⇒ const;
               itermVar(var)⇒ f var;
               itermAdd(left,right)⇒ rec1,rec2.rec1 + rec2;
               itermSubtract(left,right)⇒ rec3,rec4.rec3 - rec4;
               itermMultiply(left,right)⇒ rec5,rec6.rec5 * rec6;
               itermMinus(num)⇒ rec7.-rec7)  - int_term_ind(y;
                                                             itermConstant(const)⇒ const;
                                                             itermVar(var)⇒ f var;
                                                             itermAdd(left,right)⇒ rec1,rec2.rec1 + rec2;
                                                             itermSubtract(left,right)⇒ rec3,rec4.rec3 - rec4;
                                                             itermMultiply(left,right)⇒ rec5,rec6.rec5 * rec6;
                                                             itermMinus(num)⇒ rec7.-rec7)  
~ int_term_ind(x;
               itermConstant(n)⇒ n;
               itermVar(v)⇒ f v;
               itermAdd(l,r)⇒ rl,rr.rl + rr;
               itermSubtract(l,r)⇒ rl,rr.rl - rr;
               itermMultiply(l,r)⇒ rl,rr.rl * rr;
               itermMinus(x)⇒ r.-r)  - int_term_ind(y;
                                                     itermConstant(n)⇒ n;
                                                     itermVar(v)⇒ f v;
                                                     itermAdd(l,r)⇒ rl,rr.rl + rr;
                                                     itermSubtract(l,r)⇒ rl,rr.rl - rr;
                                                     itermMultiply(l,r)⇒ rl,rr.rl * rr;
                                                     itermMinus(x)⇒ r.-r) 

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Latex:

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Latex:

1.  y  :  Top@i
2.  x  :  Top@i
3.  f  :  Top@i
\mvdash{}  int\_term\_ind(x;
                              itermConstant(const){}\mRightarrow{}  const;
                              itermVar(var){}\mRightarrow{}  f  var;
                              itermAdd(left,right){}\mRightarrow{}  rec1,rec2.rec1  +  rec2;
                              itermSubtract(left,right){}\mRightarrow{}  rec3,rec4.rec3  -  rec4;
                              itermMultiply(left,right){}\mRightarrow{}  rec5,rec6.rec5  *  rec6;
                              itermMinus(num){}\mRightarrow{}  rec7.-rec7)   
-  int\_term\_ind(y;
                              itermConstant(const){}\mRightarrow{}  const;
                              itermVar(var){}\mRightarrow{}  f  var;
                              itermAdd(left,right){}\mRightarrow{}  rec1,rec2.rec1  +  rec2;
                              itermSubtract(left,right){}\mRightarrow{}  rec3,rec4.rec3  -  rec4;
                              itermMultiply(left,right){}\mRightarrow{}  rec5,rec6.rec5  *  rec6;
                              itermMinus(num){}\mRightarrow{}  rec7.-rec7)    \msim{}  int\_term\_value(f;x)  -  int\_term\_value(f;y)


By

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Latex:
Try  (RW  (AddrC  [2]  (UnfoldC  `int\_term\_value`))  0)\mcdot{}

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