Expression of type Equals

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 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.logic import Equals
from proveit.numbers import Mult

# build up the expression from sub-expressions
expr = Equals(Len(operands = [f_i_to_j__1_to_n]), Mult(n, i_to_j_len)).with_wrapping_at(1)

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())

\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}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(1)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	12, 10
9	ExprRange	lambda_map: 11 start_index: 17 end_index: 12
10	Operation	operator: 13 operands: 14
11	Lambda	parameter: 29 body: 15
12	Variable
13	Literal
14	ExprTuple	19, 16, 17
15	ExprRange	lambda_map: 18 start_index: 23 end_index: 19
16	Operation	operator: 20 operand: 23
17	Literal
18	Lambda	parameter: 28 body: 22
19	Variable
20	Literal
21	ExprTuple	23
22	Operation	operator: 24 operand: 28
23	Variable
24	IndexedVar	variable: 26 index: 29
25	ExprTuple	28
26	Variable
27	ExprTuple	29
28	Variable
29	Variable