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 ExprRange, Function, Variable, f, fi, i, j
from proveit.core_expr_types import f_i_to_jp1
from proveit.logic import Equals
from proveit.numbers import Add, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals([f_i_to_jp1], [fi, ExprRange(sub_expr1, Function(f, [sub_expr1]), Add(i, one), Add(j, one))]).with_wrapping_at(2)

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\left(i\right), f\left(i + 1\right), \ldots, f\left(j + 1\right)\right) =  \\ \left(f\left(i\right),f\left(i + 1\right), f\left(i + 2\right), \ldots, f\left(j + 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.	()	(2)	('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	ExprTuple	5
4	ExprTuple	6, 7
5	ExprRange	lambda_map: 9 start_index: 18 end_index: 11
6	Operation	operator: 16 operand: 18
7	ExprRange	lambda_map: 9 start_index: 10 end_index: 11
8	ExprTuple	18
9	Lambda	parameter: 21 body: 12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operand: 21
13	ExprTuple	18, 20
14	Literal
15	ExprTuple	19, 20
16	Variable
17	ExprTuple	21
18	Variable
19	Variable
20	Literal
21	Variable