# ä½�ä¸�_1 - y ≥ 2 ∧ ¬ P(x) ∧ y<x ⇒¬...

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y:=2 y<x r(x,y)=0 y:=y+1 B F G T z=false E H : z=true F T C A D

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P(x)( x ( P(x)=2 y<x y N r(x, y) 0 ¬ P(x)= 5 y (2 y<x y N r(x, y)=0) O ( ( (X): x>2 ( ( (X, Z): = ¬ = false z x P true z x P ) ( ) ( : B ( P(X, Y): x>2 y 2 [(P(x) y x) XOR ( ¬ P(x) y<x)] ( A B R(X, Y)=true, r(X, Y)=(X, 2) O ( (X) P(X, 2) ( x>2 x>2 2 2 [ (P(x) 2 x) XOR ( ¬ P(x) 2<x)] ( =[ x>2 P(x)] XOR [x>2 ∧¬ P(x)] =( x>2) ( P(x) XOR ¬ P(x)) =( x>2) T =( x>2) ( B D E H R(X, Y)=[ y<x r(x, y)=0] , z=false O P(X, Y) [ y<x r(x, y)=0] ⇒Ψ (X, false) ( x>2 y 2 [(P(x) y x) XOR ( ¬ P(x) y<x)] [ y<x r(x, y)=0] ⇒¬ P(x) ( = x>2 y 2 [(P(x) y x) XOR ( ¬ P(x) y<x)] ∧¬ P(x)
= x>2
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Unformatted text preview: y ≥ 2 ∧ ¬ P(x) ∧ y<x ⇒¬ P(x) ( B → C → H( R(X, Y)=[ y ≥ x] , z=true P(X, Y) ∧ [ y ≥ x] ⇒ Ψ (X, true) ( x>2 ∧ y ≥ 2 ∧ [(P(x) ∧ y ≤ x) XOR ( ¬ P(x) ∧ y<x)] ∧ [ y ≥ x] ⇒ P(x) ( = x>2 ∧ y ≥ 2 ∧ P(x) ∧ (y=x) ⇒ P(x) ( B → D → G → B( R(X, Y)=[ y<x ∧ r(x, y) ≠ 0] , r(X, Y)=(x, y+1) O P(X, Y) ∧ [ y<x ∧ r(x, y) ≠ 0] ⇒ P(X, y+1) ( x>2 ∧ y ≥ 2 ∧ [(P(x) ∧ y ≤ x) XOR ( ¬ P(x) ∧ y<x)] ∧ [ y<x ∧ r(x, y) ≠ 0] ⇒ x>2 ∧ y+1 ≥ 2 ∧ [(P(x) ∧ y+1 ≤ x) XOR ( ¬ P(x) ∧ y+1<x)]...
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## This note was uploaded on 10/20/2009 for the course CS G22 taught by Professor Sam during the Fall '06 term at Academy of Art University.

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ä½�ä¸�_1 - y ≥ 2 ∧ ¬ P(x) ∧ y<x ⇒¬...

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