Expression of type Equals

from the theory of proveit.logic.sets.membership

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
from proveit.logic import Equals, InSet, Or, Set
from proveit.numbers import Add, one, three

# build up the expression from sub-expressions
sub_expr1 = Add(one, three)
expr = Equals(InSet(a, Set(one, sub_expr1, three)), Or(Equals(a, one), Equals(a, sub_expr1), Equals(a, three))).with_wrapping_at(2)

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 \in \left\{1, 1 + 3, 3\right\}\right) =  \\ \left(\left(a = 1\right) \lor \left(a = \left(1 + 3\right)\right) \lor \left(a = 3\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.	()	(2)	('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: 16 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	19, 8
6	Literal
7	ExprTuple	9, 10, 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 16 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Literal
13	ExprTuple	22, 18, 23
14	ExprTuple	19, 22
15	ExprTuple	19, 18
16	Literal
17	ExprTuple	19, 23
18	Operation	operator: 20 operands: 21
19	Variable
20	Literal
21	ExprTuple	22, 23
22	Literal
23	Literal