Expression of type SubsetEq

from the theory of proveit.logic.sets.comprehension

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.core_expr_types import R__x_1_to_n, S_1_to_n, f__x_1_to_n, x_1_to_n
from proveit.logic import SetOfAll, SubsetEq
from proveit.logic.sets import general_comprehension_fyn

# build up the expression from sub-expressions
expr = SubsetEq(SetOfAll(instance_param_or_params = [x_1_to_n], instance_element = f__x_1_to_n, domains = [S_1_to_n], condition = R__x_1_to_n), general_comprehension_fyn).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\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right)~|~R\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right\}_{\left(x_{1} \in S_{1}\right), \left(x_{2} \in S_{2}\right), \ldots, \left(x_{n} \in S_{n}\right)} \subseteq  \\ \left\{f\left(y_{1}, y_{2}, \ldots, y_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right\}_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\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: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameters: 26 body: 10
9	Lambda	parameters: 29 body: 11
10	Conditional	value: 12 condition: 13
11	Conditional	value: 14 condition: 15
12	Operation	operator: 17 operands: 26
13	Operation	operator: 18 operands: 16
14	Operation	operator: 17 operands: 29
15	Operation	operator: 18 operands: 19
16	ExprTuple	20, 21
17	Variable
18	Literal
19	ExprTuple	22, 23
20	ExprRange	lambda_map: 24 start_index: 39 end_index: 40
21	Operation	operator: 25 operands: 26
22	ExprRange	lambda_map: 27 start_index: 39 end_index: 40
23	Operation	operator: 28 operands: 29
24	Lambda	parameter: 48 body: 30
25	Variable
26	ExprTuple	31
27	Lambda	parameter: 48 body: 32
28	Variable
29	ExprTuple	33
30	Operation	operator: 36 operands: 34
31	ExprRange	lambda_map: 35 start_index: 39 end_index: 40
32	Operation	operator: 36 operands: 37
33	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
34	ExprTuple	41, 42
35	Lambda	parameter: 48 body: 41
36	Literal
37	ExprTuple	43, 42
38	Lambda	parameter: 48 body: 43
39	Literal
40	Variable
41	IndexedVar	variable: 44 index: 48
42	IndexedVar	variable: 45 index: 48
43	IndexedVar	variable: 46 index: 48
44	Variable
45	Variable
46	Variable
47	ExprTuple	48
48	Variable