from z3 import *

# lecture 15 slide 5
# simple logic, substitutions, simplifications 
T = BoolVal(True)
F = BoolVal(False)
x = Bool('x')
y = Bool('y')
z = Bool('z')
w = Bool('w')

f = And(Not(x), Not(y))
g = substitute(f, (x, z))
h = substitute(f, (x, T))
j = simplify(h)
k = simplify(substitute(f, (y, F)))
l = simplify(substitute(f, (x, Not(w)), (y, F)))

# lecture 15 slide 11
# existential quantifier elimination
 
exists_y_f = Exists([y], f)
quant_elim = Tactic('qe')
qe_exists_y_f = quant_elim(exists_y_f)[0][0]

# why double nested list?
# could use multiple tactics and then get a list of results
# e.g. could do this, but not needed here: Tactic('qe', 'reduce')