Expression of type Lambda

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 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, InSet
from proveit.logic.sets import general_comprehension_fyn

# build up the expression from sub-expressions
expr = Lambda([S_1_to_n, Q, f, x], Equals(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(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) \\  = \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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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