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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 37 body: 2
1	ExprTuple	37
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 38 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	37, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	12, 13, 14
11	Conditional	value: 15 condition: 16
12	ExprRange	lambda_map: 17 start_index: 51 end_index: 37
13	ExprRange	lambda_map: 18 start_index: 51 end_index: 37
14	ExprRange	lambda_map: 19 start_index: 51 end_index: 37
15	Operation	operator: 20 operands: 21
16	Operation	operator: 22 operands: 23
17	Lambda	parameter: 62 body: 24
18	Lambda	parameter: 62 body: 58
19	Lambda	parameter: 62 body: 49
20	Literal
21	ExprTuple	25, 26
22	Literal
23	ExprTuple	27
24	IndexedVar	variable: 56 index: 62
25	Operation	operator: 28 operands: 29
26	Operation	operator: 46 operands: 30
27	ExprRange	lambda_map: 31 start_index: 51 end_index: 37
28	Literal
29	ExprTuple	32
30	ExprTuple	33
31	Lambda	parameter: 62 body: 34
32	ExprRange	lambda_map: 35 start_index: 51 end_index: 37
33	ExprRange	lambda_map: 36 start_index: 51 end_index: 37
34	Operation	operator: 38 operands: 39
35	Lambda	parameter: 59 body: 40
36	Lambda	parameter: 62 body: 41
37	Variable
38	Literal
39	ExprTuple	41, 42
40	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
41	Operation	operator: 46 operands: 47
42	Literal
43	Lambda	parameter: 62 body: 48
44	IndexedVar	variable: 60 index: 59
45	IndexedVar	variable: 53 index: 59
46	Literal
47	ExprTuple	49, 50, 51
48	Operation	operator: 52 operand: 62
49	IndexedVar	variable: 53 index: 62
50	Operation	operator: 54 operand: 58
51	Literal
52	IndexedVar	variable: 56 index: 59
53	Variable
54	Literal
55	ExprTuple	58
56	Variable
57	ExprTuple	59
58	IndexedVar	variable: 60 index: 62
59	Variable
60	Variable
61	ExprTuple	62
62	Variable