Expression of type ExprTuple

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 import ExprTuple, Lambda, Q, f, x
from proveit.core_expr_types import Q__y_1_to_n, S_1_to_n, f__y_1_to_n, y_1_to_n
from proveit.logic import Equals, Exists, Implies, InSet
from proveit.logic.sets import general_comprehension_fyn

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([S_1_to_n, Q, f, x], Implies(InSet(x, general_comprehension_fyn), Exists(instance_param_or_params = [y_1_to_n], instance_expr = Equals(x, f__y_1_to_n), domains = [S_1_to_n], condition = Q__y_1_to_n)).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())

\left(\left(S_{1}, S_{2}, \ldots, S_{n}, Q, f, x\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left(x \in \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)}\right) \\  \Rightarrow \left[\exists_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(x = f\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right)\right] \end{array} \end{array}\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	4, 32, 28, 24
3	Operation	operator: 5 operands: 6
4	ExprRange	lambda_map: 7 start_index: 39 end_index: 40
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 46 body: 41
8	Operation	operator: 36 operands: 10
9	Operation	operator: 11 operand: 14
10	ExprTuple	24, 13
11	Literal
12	ExprTuple	14
13	Operation	operator: 15 operand: 18
14	Lambda	parameters: 33 body: 17
15	Literal
16	ExprTuple	18
17	Conditional	value: 19 condition: 23
18	Lambda	parameters: 33 body: 20
19	Operation	operator: 21 operands: 22
20	Conditional	value: 25 condition: 23
21	Literal
22	ExprTuple	24, 25
23	Operation	operator: 26 operands: 27
24	Variable
25	Operation	operator: 28 operands: 33
26	Literal
27	ExprTuple	29, 30
28	Variable
29	ExprRange	lambda_map: 31 start_index: 39 end_index: 40
30	Operation	operator: 32 operands: 33
31	Lambda	parameter: 46 body: 34
32	Variable
33	ExprTuple	35
34	Operation	operator: 36 operands: 37
35	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
36	Literal
37	ExprTuple	42, 41
38	Lambda	parameter: 46 body: 42
39	Literal
40	Variable
41	IndexedVar	variable: 43 index: 46
42	IndexedVar	variable: 44 index: 46
43	Variable
44	Variable
45	ExprTuple	46
46	Variable