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, Implies, 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], Implies(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), InSet(x, general_comprehension_fyn)).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[\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] \\  \Rightarrow \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) \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, 31, 25, 22
2	Operation	operator: 4 operands: 5
3	ExprRange	lambda_map: 6 start_index: 38 end_index: 39
4	Literal
5	ExprTuple	7, 8
6	Lambda	parameter: 45 body: 40
7	Operation	operator: 9 operand: 12
8	Operation	operator: 35 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	22, 13
12	Lambda	parameters: 32 body: 14
13	Operation	operator: 15 operand: 18
14	Conditional	value: 17 condition: 24
15	Literal
16	ExprTuple	18
17	Operation	operator: 19 operands: 20
18	Lambda	parameters: 32 body: 21
19	Literal
20	ExprTuple	22, 23
21	Conditional	value: 23 condition: 24
22	Variable
23	Operation	operator: 25 operands: 32
24	Operation	operator: 26 operands: 27
25	Variable
26	Literal
27	ExprTuple	28, 29
28	ExprRange	lambda_map: 30 start_index: 38 end_index: 39
29	Operation	operator: 31 operands: 32
30	Lambda	parameter: 45 body: 33
31	Variable
32	ExprTuple	34
33	Operation	operator: 35 operands: 36
34	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
35	Literal
36	ExprTuple	41, 40
37	Lambda	parameter: 45 body: 41
38	Literal
39	Variable
40	IndexedVar	variable: 42 index: 45
41	IndexedVar	variable: 43 index: 45
42	Variable
43	Variable
44	ExprTuple	45
45	Variable