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, R, f
from proveit.core_expr_types import Q__x_1_to_n, R__x_1_to_n, S_1_to_n, f__x_1_to_n, x_1_to_n
from proveit.logic import Forall, Implies, SetOfAll, SubsetEq
from proveit.logic.sets import general_comprehension_fyn

# build up the expression from sub-expressions
sub_expr1 = [x_1_to_n]
sub_expr2 = [S_1_to_n]
expr = Lambda([f, Q, R, S_1_to_n], Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Q__x_1_to_n, domains = sub_expr2, condition = R__x_1_to_n), SubsetEq(SetOfAll(instance_param_or_params = sub_expr1, instance_element = f__x_1_to_n, domains = sub_expr2, condition = R__x_1_to_n), general_comprehension_fyn).with_wrapping_at(2)).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())

\left(f, Q, R, S_{1}, S_{2}, \ldots, S_{n}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left[\forall_{\left(x_{1} \in S_{1}\right), \left(x_{2} \in S_{2}\right), \ldots, \left(x_{n} \in S_{n}\right)~|~R\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \Rightarrow  \\ \left(\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}\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	30, 41, 38, 3
2	Operation	operator: 4 operands: 5
3	ExprRange	lambda_map: 6 start_index: 52 end_index: 53
4	Literal
5	ExprTuple	7, 8
6	Lambda	parameter: 61 body: 55
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	14, 15
13	Lambda	parameters: 39 body: 16
14	Operation	operator: 18 operand: 21
15	Operation	operator: 18 operand: 22
16	Conditional	value: 20 condition: 26
17	ExprTuple	21
18	Literal
19	ExprTuple	22
20	Operation	operator: 41 operands: 39
21	Lambda	parameters: 39 body: 23
22	Lambda	parameters: 42 body: 24
23	Conditional	value: 25 condition: 26
24	Conditional	value: 27 condition: 28
25	Operation	operator: 30 operands: 39
26	Operation	operator: 31 operands: 29
27	Operation	operator: 30 operands: 42
28	Operation	operator: 31 operands: 32
29	ExprTuple	33, 34
30	Variable
31	Literal
32	ExprTuple	35, 36
33	ExprRange	lambda_map: 37 start_index: 52 end_index: 53
34	Operation	operator: 38 operands: 39
35	ExprRange	lambda_map: 40 start_index: 52 end_index: 53
36	Operation	operator: 41 operands: 42
37	Lambda	parameter: 61 body: 43
38	Variable
39	ExprTuple	44
40	Lambda	parameter: 61 body: 45
41	Variable
42	ExprTuple	46
43	Operation	operator: 49 operands: 47
44	ExprRange	lambda_map: 48 start_index: 52 end_index: 53
45	Operation	operator: 49 operands: 50
46	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
47	ExprTuple	54, 55
48	Lambda	parameter: 61 body: 54
49	Literal
50	ExprTuple	56, 55
51	Lambda	parameter: 61 body: 56
52	Literal
53	Variable
54	IndexedVar	variable: 57 index: 61
55	IndexedVar	variable: 58 index: 61
56	IndexedVar	variable: 59 index: 61
57	Variable
58	Variable
59	Variable
60	ExprTuple	61
61	Variable