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, i, n
from proveit.core_expr_types import Len
from proveit.core_expr_types.tuples import f_1_to_i__1_to_n
from proveit.numbers import Mult

# build up the expression from sub-expressions
expr = ExprTuple(Len(operands = [f_1_to_i__1_to_n]), Mult(n, i))

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(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)|, n \cdot i\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	9, 13
7	ExprRange	lambda_map: 8 start_index: 12 end_index: 9
8	Lambda	parameter: 20 body: 10
9	Variable
10	ExprRange	lambda_map: 11 start_index: 12 end_index: 13
11	Lambda	parameter: 19 body: 14
12	Literal
13	Variable
14	Operation	operator: 15 operand: 19
15	IndexedVar	variable: 17 index: 20
16	ExprTuple	19
17	Variable
18	ExprTuple	20
19	Variable
20	Variable