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
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 And, Equals

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f_1_to_n, i_1_to_n, j_1_to_n], 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(\left(f_{1}, f_{2}, \ldots, f_{n}, i_{1}, i_{2}, \ldots, i_{n}, j_{1}, j_{2}, \ldots, j_{n}\right) \mapsto \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..\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	parameters: 2 body: 3
2	ExprTuple	4, 5, 6
3	Conditional	value: 7 condition: 8
4	ExprRange	lambda_map: 9 start_index: 43 end_index: 29
5	ExprRange	lambda_map: 10 start_index: 43 end_index: 29
6	ExprRange	lambda_map: 11 start_index: 43 end_index: 29
7	Operation	operator: 12 operands: 13
8	Operation	operator: 14 operands: 15
9	Lambda	parameter: 54 body: 16
10	Lambda	parameter: 54 body: 50
11	Lambda	parameter: 54 body: 41
12	Literal
13	ExprTuple	17, 18
14	Literal
15	ExprTuple	19
16	IndexedVar	variable: 48 index: 54
17	Operation	operator: 20 operands: 21
18	Operation	operator: 38 operands: 22
19	ExprRange	lambda_map: 23 start_index: 43 end_index: 29
20	Literal
21	ExprTuple	24
22	ExprTuple	25
23	Lambda	parameter: 54 body: 26
24	ExprRange	lambda_map: 27 start_index: 43 end_index: 29
25	ExprRange	lambda_map: 28 start_index: 43 end_index: 29
26	Operation	operator: 30 operands: 31
27	Lambda	parameter: 51 body: 32
28	Lambda	parameter: 54 body: 33
29	Variable
30	Literal
31	ExprTuple	33, 34
32	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
33	Operation	operator: 38 operands: 39
34	Literal
35	Lambda	parameter: 54 body: 40
36	IndexedVar	variable: 52 index: 51
37	IndexedVar	variable: 45 index: 51
38	Literal
39	ExprTuple	41, 42, 43
40	Operation	operator: 44 operand: 54
41	IndexedVar	variable: 45 index: 54
42	Operation	operator: 46 operand: 50
43	Literal
44	IndexedVar	variable: 48 index: 51
45	Variable
46	Literal
47	ExprTuple	50
48	Variable
49	ExprTuple	51
50	IndexedVar	variable: 52 index: 54
51	Variable
52	Variable
53	ExprTuple	54
54	Variable