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Step * 1 of Lemma int_formual_prop_imp_lemma


1. y : Top@i
2. x : Top@i
3. f : Top@i
⊢ int_formula_prop(f;x "=>" y) ~ int_formula_prop(f;x) ⇒ int_formula_prop(f;y)
BY
{ Try (RW (AddrC [1] (UnfoldC `int_formula_prop` ANDTHENC ReduceC)) 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_prop(f;x) ⇒ int_formula_prop(f;y)

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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\_prop(f;x  "=>"  y)  \msim{}  int\_formula\_prop(f;x)  {}\mRightarrow{}  int\_formula\_prop(f;y)


By

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Latex:
Try  (RW  (AddrC  [1]  (UnfoldC  `int\_formula\_prop`  ANDTHENC  ReduceC))  0)\mcdot{}

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