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Step * 1 1 of Lemma int_formula_prop_not_lemma


1. x : Top@i
2. 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_prop(f;x)
BY
{ Try (RW (AddrC [2] (UnfoldC `int_formula_prop`)) 0)⋅ }

1
1. x : Top@i
2. 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(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)

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Latex:

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Latex:

1.  x  :  Top@i
2.  f  :  Top@i
\mvdash{}  \mneg{}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)    \msim{}  \mneg{}int\_formula\_prop(f;x)


By

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

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