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Step * 1 1 of Lemma int_formula_prop_or_lemma


1. y : Top@i
2. x : Top@i
3. f : Top@i
⊢ int_formula_ind(x;
                  intformless(left,right)⇒ int_term_value(f;left) < int_term_value(f;right);
                  intformle(left,right)⇒ int_term_value(f;left) ≤ int_term_value(f;right);
                  intformeq(left,right)⇒ int_term_value(f;left) = int_term_value(f;right) ∈ ℤ;
                  intformand(left,right)⇒ rec1,rec2.rec1 ∧ rec2;
                  intformor(left,right)⇒ rec3,rec4.rec3 ∨ rec4;
                  intformimplies(left,right)⇒ rec5,rec6.rec5 ⇒ rec6;
                  intformnot(form)⇒ rec7.¬rec7) 
∨ int_formula_ind(y;
                  intformless(left,right)⇒ int_term_value(f;left) < int_term_value(f;right);
                  intformle(left,right)⇒ int_term_value(f;left) ≤ int_term_value(f;right);
                  intformeq(left,right)⇒ int_term_value(f;left) = int_term_value(f;right) ∈ ℤ;
                  intformand(left,right)⇒ rec1,rec2.rec1 ∧ rec2;
                  intformor(left,right)⇒ rec3,rec4.rec3 ∨ rec4;
                  intformimplies(left,right)⇒ rec5,rec6.rec5 ⇒ rec6;
                  intformnot(form)⇒ rec7.¬rec7)  ~ int_formula_prop(f;x) ∨ int_formula_prop(f;y)
BY
{ Try (RW (AddrC [2] (UnfoldC `int_formula_prop`)) 0)⋅ }

1
1. y : Top@i
2. x : Top@i
3. f : Top@i
⊢ int_formula_ind(x;
                  intformless(left,right)⇒ int_term_value(f;left) < int_term_value(f;right);
                  intformle(left,right)⇒ int_term_value(f;left) ≤ int_term_value(f;right);
                  intformeq(left,right)⇒ int_term_value(f;left) = int_term_value(f;right) ∈ ℤ;
                  intformand(left,right)⇒ rec1,rec2.rec1 ∧ rec2;
                  intformor(left,right)⇒ rec3,rec4.rec3 ∨ rec4;
                  intformimplies(left,right)⇒ rec5,rec6.rec5 ⇒ rec6;
                  intformnot(form)⇒ rec7.¬rec7) 
∨ int_formula_ind(y;
                  intformless(left,right)⇒ int_term_value(f;left) < int_term_value(f;right);
                  intformle(left,right)⇒ int_term_value(f;left) ≤ int_term_value(f;right);
                  intformeq(left,right)⇒ int_term_value(f;left) = int_term_value(f;right) ∈ ℤ;
                  intformand(left,right)⇒ rec1,rec2.rec1 ∧ rec2;
                  intformor(left,right)⇒ rec3,rec4.rec3 ∨ rec4;
                  intformimplies(left,right)⇒ rec5,rec6.rec5 ⇒ rec6;
                  intformnot(form)⇒ rec7.¬rec7)  ~ int_formula_ind(x;
                                                                    a,b.int_term_value(f;a) < int_term_value(f;b);
                                                                    a,b.int_term_value(f;a) ≤ int_term_value(f;b);
                                                                    a,b.int_term_value(f;a) = int_term_value(f;b) ∈ ℤ;
                                                                    X,Y,PX,PY.PX ∧ PY;
                                                                    X,Y,PX,PY.PX ∨ PY;
                                                                    X,Y,PX,PY.PX ⇒ PY;
                                                                    X,PX.¬PX)
∨ int_formula_ind(y;
                  a,b.int_term_value(f;a) < int_term_value(f;b);
                  a,b.int_term_value(f;a) ≤ int_term_value(f;b);
                  a,b.int_term_value(f;a) = int_term_value(f;b) ∈ ℤ;
                  X,Y,PX,PY.PX ∧ PY;
                  X,Y,PX,PY.PX ∨ PY;
                  X,Y,PX,PY.PX ⇒ PY;
                  X,PX.¬PX)

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Latex:

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Latex:

1.  y  :  Top@i
2.  x  :  Top@i
3.  f  :  Top@i
\mvdash{}  int\_formula\_ind(x;
                                    intformless(left,right){}\mRightarrow{}  int\_term\_value(f;left)  <  int\_term\_value(f;right);
                                    intformle(left,right){}\mRightarrow{}  int\_term\_value(f;left)  \mleq{}  int\_term\_value(f;right);
                                    intformeq(left,right){}\mRightarrow{}  int\_term\_value(f;left)  =  int\_term\_value(f;right);
                                    intformand(left,right){}\mRightarrow{}  rec1,rec2.rec1  \mwedge{}  rec2;
                                    intformor(left,right){}\mRightarrow{}  rec3,rec4.rec3  \mvee{}  rec4;
                                    intformimplies(left,right){}\mRightarrow{}  rec5,rec6.rec5  {}\mRightarrow{}  rec6;
                                    intformnot(form){}\mRightarrow{}  rec7.\mneg{}rec7) 
\mvee{}  int\_formula\_ind(y;
                                    intformless(left,right){}\mRightarrow{}  int\_term\_value(f;left)  <  int\_term\_value(f;right);
                                    intformle(left,right){}\mRightarrow{}  int\_term\_value(f;left)  \mleq{}  int\_term\_value(f;right);
                                    intformeq(left,right){}\mRightarrow{}  int\_term\_value(f;left)  =  int\_term\_value(f;right);
                                    intformand(left,right){}\mRightarrow{}  rec1,rec2.rec1  \mwedge{}  rec2;
                                    intformor(left,right){}\mRightarrow{}  rec3,rec4.rec3  \mvee{}  rec4;
                                    intformimplies(left,right){}\mRightarrow{}  rec5,rec6.rec5  {}\mRightarrow{}  rec6;
                                    intformnot(form){}\mRightarrow{}  rec7.\mneg{}rec7)    \msim{}  int\_formula\_prop(f;x)  \mvee{}  int\_formula\_prop(f;y)


By

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

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