Step * 1 of Lemma int_formula_prop_and_lemma


1. Top@i
2. Top@i
3. 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. Top@i
2. Top@i
3. 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)


Latex:


Latex:

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


By


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




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