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 ExprTuple, n
from proveit.core_expr_types import Len, i_to_j_len
from proveit.core_expr_types.tuples import f_i_to_j__1_to_n
from proveit.numbers import Mult

# build up the expression from sub-expressions
expr = ExprTuple(Len(operands = [f_i_to_j__1_to_n]), Mult(n, i_to_j_len))

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}\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)|, n \cdot \left(j - i + 1\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	10, 8
7	ExprRange	lambda_map: 9 start_index: 15 end_index: 10
8	Operation	operator: 11 operands: 12
9	Lambda	parameter: 27 body: 13
10	Variable
11	Literal
12	ExprTuple	17, 14, 15
13	ExprRange	lambda_map: 16 start_index: 21 end_index: 17
14	Operation	operator: 18 operand: 21
15	Literal
16	Lambda	parameter: 26 body: 20
17	Variable
18	Literal
19	ExprTuple	21
20	Operation	operator: 22 operand: 26
21	Variable
22	IndexedVar	variable: 24 index: 27
23	ExprTuple	26
24	Variable
25	ExprTuple	27
26	Variable
27	Variable