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, n
from proveit.core_expr_types import Len, f_1_to_n
from proveit.core_expr_types.tuples import f_1_to_i__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], Conditional(Equals(Len(operands = [f_1_to_i__1_to_n]), Mult(n, i)).with_wrapping_at(1), InSet(i, 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\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} |\left(f_{1}\left(1\right), f_{1}\left(2\right), \ldots, f_{1}\left(i\right), f_{2}\left(1\right), f_{2}\left(2\right), \ldots, f_{2}\left(i\right), \ldots\ldots, f_{n}\left(1\right), f_{n}\left(2\right), \ldots, f_{n}\left(i\right)\right)| \\  = \left(n \cdot i\right) \end{array} \end{array} \textrm{ if } i \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, 26
3	Conditional	value: 5 condition: 6
4	ExprRange	lambda_map: 7 start_index: 25 end_index: 22
5	Operation	operator: 8 operands: 9
6	Operation	operator: 10 operands: 11
7	Lambda	parameter: 32 body: 12
8	Literal
9	ExprTuple	13, 14
10	Literal
11	ExprTuple	26, 15
12	IndexedVar	variable: 30 index: 32
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	22, 26
20	ExprRange	lambda_map: 21 start_index: 25 end_index: 22
21	Lambda	parameter: 33 body: 23
22	Variable
23	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
24	Lambda	parameter: 32 body: 27
25	Literal
26	Variable
27	Operation	operator: 28 operand: 32
28	IndexedVar	variable: 30 index: 33
29	ExprTuple	32
30	Variable
31	ExprTuple	33
32	Variable
33	Variable