Expression of type Conditional

from the theory of proveit.logic.sets.equivalence

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, B, Conditional
from proveit.logic import And, FALSE, SetEquiv, SetNotEquiv

# build up the expression from sub-expressions
expr = Conditional(FALSE, And(SetEquiv(A, B), SetNotEquiv(A, B)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\bot \textrm{ if } A \cong B ,  A \ncong B\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Literal
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operands: 9
6	Operation	operator: 8 operands: 9
7	Literal
8	Literal
9	ExprTuple	10, 11
10	Variable
11	Variable