Expression of type Conditional

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, 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 = 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\{\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 36 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	35, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	10, 11, 12
9	Conditional	value: 13 condition: 14
10	ExprRange	lambda_map: 15 start_index: 49 end_index: 35
11	ExprRange	lambda_map: 16 start_index: 49 end_index: 35
12	ExprRange	lambda_map: 17 start_index: 49 end_index: 35
13	Operation	operator: 18 operands: 19
14	Operation	operator: 20 operands: 21
15	Lambda	parameter: 60 body: 22
16	Lambda	parameter: 60 body: 56
17	Lambda	parameter: 60 body: 47
18	Literal
19	ExprTuple	23, 24
20	Literal
21	ExprTuple	25
22	IndexedVar	variable: 54 index: 60
23	Operation	operator: 26 operands: 27
24	Operation	operator: 44 operands: 28
25	ExprRange	lambda_map: 29 start_index: 49 end_index: 35
26	Literal
27	ExprTuple	30
28	ExprTuple	31
29	Lambda	parameter: 60 body: 32
30	ExprRange	lambda_map: 33 start_index: 49 end_index: 35
31	ExprRange	lambda_map: 34 start_index: 49 end_index: 35
32	Operation	operator: 36 operands: 37
33	Lambda	parameter: 57 body: 38
34	Lambda	parameter: 60 body: 39
35	Variable
36	Literal
37	ExprTuple	39, 40
38	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
39	Operation	operator: 44 operands: 45
40	Literal
41	Lambda	parameter: 60 body: 46
42	IndexedVar	variable: 58 index: 57
43	IndexedVar	variable: 51 index: 57
44	Literal
45	ExprTuple	47, 48, 49
46	Operation	operator: 50 operand: 60
47	IndexedVar	variable: 51 index: 60
48	Operation	operator: 52 operand: 56
49	Literal
50	IndexedVar	variable: 54 index: 57
51	Variable
52	Literal
53	ExprTuple	56
54	Variable
55	ExprTuple	57
56	IndexedVar	variable: 58 index: 60
57	Variable
58	Variable
59	ExprTuple	60
60	Variable