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 x
from proveit.core_expr_types import A_1_to_m, a_1_to_m
from proveit.logic import And, CartProd, Equals, InSet
from proveit.logic.sets.cartesian_products import a_in_A__1_to_m

# build up the expression from sub-expressions
expr = Equals(InSet(x, CartProd(A_1_to_m)), And(Equals(x, [a_1_to_m]), a_in_A__1_to_m)).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(x \in \left(A_{1} \times  A_{2} \times  \ldots \times  A_{m}\right)\right) =  \\ \left(\left(x = \left(a_{1}, a_{2}, \ldots, a_{m}\right)\right)\land \left(a_{1} \in A_{1}\right) \land  \left(a_{2} \in A_{2}\right) \land  \ldots \land  \left(a_{m} \in A_{m}\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: 12 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 21 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	16, 7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprRange	lambda_map: 14 start_index: 24 end_index: 25
10	Literal
11	ExprTuple	15
12	Literal
13	ExprTuple	16, 17
14	Lambda	parameter: 31 body: 18
15	ExprRange	lambda_map: 19 start_index: 24 end_index: 25
16	Variable
17	ExprTuple	20
18	Operation	operator: 21 operands: 22
19	Lambda	parameter: 31 body: 26
20	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
21	Literal
22	ExprTuple	27, 26
23	Lambda	parameter: 31 body: 27
24	Literal
25	Variable
26	IndexedVar	variable: 28 index: 31
27	IndexedVar	variable: 29 index: 31
28	Variable
29	Variable
30	ExprTuple	31
31	Variable