Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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