Expression of type ExprTuple

from the theory of proveit.core_expr_types.tuples

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, ExprTuple, Lambda, n
from proveit.core_expr_types import Len, f_1_to_n, i_1_to_n, j_1_to_n
from proveit.core_expr_types.tuples import f_ik_to_jk__1_to_n, range_len_conditions, range_len_sum
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [f_1_to_n, i_1_to_n, j_1_to_n], instance_expr = Equals(Len(operands = [f_ik_to_jk__1_to_n]), range_len_sum).with_wrapping_at(1), condition = range_len_conditions).with_wrapping(), 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())

\left(n \mapsto \left\{\begin{array}{l}\forall_{f_{1}, f_{2}, \ldots, f_{n}, i_{1}, i_{2}, \ldots, i_{n}, j_{1}, j_{2}, \ldots, j_{n}~|~\left(\left(j_{1} - i_{1} + 1\right) \in \mathbb{N}\right), \left(\left(j_{2} - i_{2} + 1\right) \in \mathbb{N}\right), \ldots, \left(\left(j_{n} - i_{n} + 1\right) \in \mathbb{N}\right)}~\\
\left(\begin{array}{c} \begin{array}{l} |\left(f_{1}\left(i_{1}\right), f_{1}\left(i_{1} + 1\right), \ldots, f_{1}\left(j_{1}\right), f_{2}\left(i_{2}\right), f_{2}\left(i_{2} + 1\right), \ldots, f_{2}\left(j_{2}\right), \ldots\ldots, f_{n}\left(i_{n}\right), f_{n}\left(i_{n} + 1\right), \ldots, f_{n}\left(j_{n}\right)\right)| \\  = \left(\left(j_{1} - i_{1} + 1\right) +  \left(j_{2} - i_{2} + 1\right) +  \ldots +  \left(j_{n} - i_{n} + 1\right)\right) \end{array} \end{array}\right)\end{array} \textrm{ if } n \in \mathbb{N}^+\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	parameter: 38 body: 3
2	ExprTuple	38
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 39 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	38, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	13, 14, 15
12	Conditional	value: 16 condition: 17
13	ExprRange	lambda_map: 18 start_index: 52 end_index: 38
14	ExprRange	lambda_map: 19 start_index: 52 end_index: 38
15	ExprRange	lambda_map: 20 start_index: 52 end_index: 38
16	Operation	operator: 21 operands: 22
17	Operation	operator: 23 operands: 24
18	Lambda	parameter: 63 body: 25
19	Lambda	parameter: 63 body: 59
20	Lambda	parameter: 63 body: 50
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	28
25	IndexedVar	variable: 57 index: 63
26	Operation	operator: 29 operands: 30
27	Operation	operator: 47 operands: 31
28	ExprRange	lambda_map: 32 start_index: 52 end_index: 38
29	Literal
30	ExprTuple	33
31	ExprTuple	34
32	Lambda	parameter: 63 body: 35
33	ExprRange	lambda_map: 36 start_index: 52 end_index: 38
34	ExprRange	lambda_map: 37 start_index: 52 end_index: 38
35	Operation	operator: 39 operands: 40
36	Lambda	parameter: 60 body: 41
37	Lambda	parameter: 63 body: 42
38	Variable
39	Literal
40	ExprTuple	42, 43
41	ExprRange	lambda_map: 44 start_index: 45 end_index: 46
42	Operation	operator: 47 operands: 48
43	Literal
44	Lambda	parameter: 63 body: 49
45	IndexedVar	variable: 61 index: 60
46	IndexedVar	variable: 54 index: 60
47	Literal
48	ExprTuple	50, 51, 52
49	Operation	operator: 53 operand: 63
50	IndexedVar	variable: 54 index: 63
51	Operation	operator: 55 operand: 59
52	Literal
53	IndexedVar	variable: 57 index: 60
54	Variable
55	Literal
56	ExprTuple	59
57	Variable
58	ExprTuple	60
59	IndexedVar	variable: 61 index: 63
60	Variable
61	Variable
62	ExprTuple	63
63	Variable