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 Conditional, Lambda, Q, f, n, 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, Forall, Implies, InSet
from proveit.logic.sets import general_comprehension_fyn
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [S_1_to_n, Q, f, x], instance_expr = 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)), InSet(n, NaturalPos)))

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())

n \mapsto \left\{\forall_{S_{1}, S_{2}, \ldots, S_{n}, Q, f, x}~\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) \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 48 body: 2
1	ExprTuple	48
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 44 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	48, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	12, 40, 34, 31
11	Operation	operator: 13 operands: 14
12	ExprRange	lambda_map: 15 start_index: 47 end_index: 48
13	Literal
14	ExprTuple	16, 17
15	Lambda	parameter: 54 body: 49
16	Operation	operator: 18 operand: 21
17	Operation	operator: 44 operands: 20
18	Literal
19	ExprTuple	21
20	ExprTuple	31, 22
21	Lambda	parameters: 41 body: 23
22	Operation	operator: 24 operand: 27
23	Conditional	value: 26 condition: 33
24	Literal
25	ExprTuple	27
26	Operation	operator: 28 operands: 29
27	Lambda	parameters: 41 body: 30
28	Literal
29	ExprTuple	31, 32
30	Conditional	value: 32 condition: 33
31	Variable
32	Operation	operator: 34 operands: 41
33	Operation	operator: 35 operands: 36
34	Variable
35	Literal
36	ExprTuple	37, 38
37	ExprRange	lambda_map: 39 start_index: 47 end_index: 48
38	Operation	operator: 40 operands: 41
39	Lambda	parameter: 54 body: 42
40	Variable
41	ExprTuple	43
42	Operation	operator: 44 operands: 45
43	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
44	Literal
45	ExprTuple	50, 49
46	Lambda	parameter: 54 body: 50
47	Literal
48	Variable
49	IndexedVar	variable: 51 index: 54
50	IndexedVar	variable: 52 index: 54
51	Variable
52	Variable
53	ExprTuple	54
54	Variable