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, i, j, n
from proveit.core_expr_types import Len, f_1_to_n, i_to_j_len
from proveit.core_expr_types.tuples import f_i_to_j__1_to_n
from proveit.logic import Equals, InSet
from proveit.numbers import Mult, Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f_1_to_n, i, j], Conditional(Equals(Len(operands = [f_i_to_j__1_to_n]), Mult(n, i_to_j_len)).with_wrapping_at(1), InSet(i_to_j_len, Natural))))

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, j\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} |\left(f_{1}\left(i\right), f_{1}\left(i + 1\right), \ldots, f_{1}\left(j\right), f_{2}\left(i\right), f_{2}\left(i + 1\right), \ldots, f_{2}\left(j\right), \ldots\ldots, f_{n}\left(i\right), f_{n}\left(i + 1\right), \ldots, f_{n}\left(j\right)\right)| \\  = \left(n \cdot \left(j - i + 1\right)\right) \end{array} \end{array} \textrm{ if } \left(j - i + 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	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	4, 34, 30
3	Conditional	value: 5 condition: 6
4	ExprRange	lambda_map: 7 start_index: 28 end_index: 23
5	Operation	operator: 8 operands: 9
6	Operation	operator: 10 operands: 11
7	Lambda	parameter: 39 body: 12
8	Literal
9	ExprTuple	13, 14
10	Literal
11	ExprTuple	21, 15
12	IndexedVar	variable: 37 index: 39
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	23, 21
20	ExprRange	lambda_map: 22 start_index: 28 end_index: 23
21	Operation	operator: 24 operands: 25
22	Lambda	parameter: 40 body: 26
23	Variable
24	Literal
25	ExprTuple	30, 27, 28
26	ExprRange	lambda_map: 29 start_index: 34 end_index: 30
27	Operation	operator: 31 operand: 34
28	Literal
29	Lambda	parameter: 39 body: 33
30	Variable
31	Literal
32	ExprTuple	34
33	Operation	operator: 35 operand: 39
34	Variable
35	IndexedVar	variable: 37 index: 40
36	ExprTuple	39
37	Variable
38	ExprTuple	40
39	Variable
40	Variable