Expression of type Equals

from the theory of proveit.logic.booleans.disjunction

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, Boolean, Equals, InSet, Not, Or

# build up the expression from sub-expressions
sub_expr1 = Or(A, B)
sub_expr2 = InSet(A, Boolean)
sub_expr3 = InSet(B, Boolean)
sub_expr4 = Not(And(Not(A), Not(B)))
expr = Equals(Conditional(sub_expr1, And(sub_expr2, And(sub_expr3, sub_expr4))), Conditional(sub_expr1, And(sub_expr2, sub_expr3, sub_expr4))).with_wrapping_at(1)

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())

\begin{array}{c} \begin{array}{l} \left\{A \lor B \textrm{ if } A \in \mathbb{B} ,  \left(B \in \mathbb{B}\right) \land (\lnot \left((\lnot A) \land (\lnot B)\right))\right.. \\  = \left\{A \lor B \textrm{ if } A \in \mathbb{B} ,  B \in \mathbb{B} ,  \lnot \left((\lnot A) \land (\lnot B)\right)\right.. \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(1)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Conditional	value: 6 condition: 5
4	Conditional	value: 6 condition: 7
5	Operation	operator: 23 operands: 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 23 operands: 11
8	ExprTuple	13, 12
9	Literal
10	ExprTuple	30, 31
11	ExprTuple	13, 16, 17
12	Operation	operator: 23 operands: 14
13	Operation	operator: 18 operands: 15
14	ExprTuple	16, 17
15	ExprTuple	30, 21
16	Operation	operator: 18 operands: 19
17	Operation	operator: 28 operand: 22
18	Literal
19	ExprTuple	31, 21
20	ExprTuple	22
21	Literal
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 28 operand: 30
26	Operation	operator: 28 operand: 31
27	ExprTuple	30
28	Literal
29	ExprTuple	31
30	Variable
31	Variable