Expression of type Equals

from the theory of proveit.logic.sets.cartesian_products

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 ExprRange, Variable, x
from proveit.logic import CartExp, CartProd, Equals, InSet
from proveit.numbers import Real, one, three

# build up the expression from sub-expressions
expr = Equals(InSet(x, CartExp(Real, three)), InSet(x, CartProd(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), Real, one, three))))

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(x \in \mathbb{R}^{3}\right) = \left(x \in \left(\mathbb{R} \times  \mathbb{R} \times  ..0 \times.. \times  \mathbb{R}\right)\right)

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.	()	()	('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	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	9, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 11 operands: 12
9	Variable
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	20, 18
13	Literal
14	ExprTuple	15
15	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
16	Lambda	parameter: 21 body: 20
17	Literal
18	Literal
19	ExprTuple	21
20	Literal
21	Variable