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
from proveit.core_expr_types import Len
from proveit.core_expr_types.tuples import f_ik_to_jk__1_to_n, range_len_conditions, range_len_sum
from proveit.logic import And, Equals

# build up the expression from sub-expressions
expr = Conditional(Equals(Len(operands = [f_ik_to_jk__1_to_n]), range_len_sum).with_wrapping_at(1), And(range_len_conditions))

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}{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} \textrm{ if } \left(\left(j_{1} - i_{1} + 1\right) \in \mathbb{N}\right) \land  \left(\left(j_{2} - i_{2} + 1\right) \in \mathbb{N}\right) \land  \ldots \land  \left(\left(j_{n} - i_{n} + 1\right) \in \mathbb{N}\right)\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 28 operands: 12
9	ExprRange	lambda_map: 13 start_index: 33 end_index: 19
10	Literal
11	ExprTuple	14
12	ExprTuple	15
13	Lambda	parameter: 44 body: 16
14	ExprRange	lambda_map: 17 start_index: 33 end_index: 19
15	ExprRange	lambda_map: 18 start_index: 33 end_index: 19
16	Operation	operator: 20 operands: 21
17	Lambda	parameter: 41 body: 22
18	Lambda	parameter: 44 body: 23
19	Variable
20	Literal
21	ExprTuple	23, 24
22	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	Lambda	parameter: 44 body: 30
26	IndexedVar	variable: 42 index: 41
27	IndexedVar	variable: 35 index: 41
28	Literal
29	ExprTuple	31, 32, 33
30	Operation	operator: 34 operand: 44
31	IndexedVar	variable: 35 index: 44
32	Operation	operator: 36 operand: 40
33	Literal
34	IndexedVar	variable: 38 index: 41
35	Variable
36	Literal
37	ExprTuple	40
38	Variable
39	ExprTuple	41
40	IndexedVar	variable: 42 index: 44
41	Variable
42	Variable
43	ExprTuple	44
44	Variable