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, a, f, k, l
from proveit.core_expr_types import f_i_to_j_dec
from proveit.logic import Equals
from proveit.numbers import Add, Neg

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals([f_i_to_j_dec], [ExprRange(sub_expr1, Function(f, [Add(Neg(sub_expr1), a)]), Neg(k), Neg(l)).with_decreasing_order()])

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(f\left(i\right), f\left(i - 1\right), \ldots, f\left(j\right)\right) = \left(f\left(k + a\right), f\left(\left(k - 1\right) + a\right), \ldots, f\left(l + a\right)\right)

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.	()	()	('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
5	ExprRange	lambda_map: 7 start_index: 8 end_index: 9
6	ExprRange	lambda_map: 10 start_index: 11 end_index: 12
7	Lambda	parameter: 33 body: 13
8	Operation	operator: 31 operand: 20
9	Operation	operator: 31 operand: 21
10	Lambda	parameter: 33 body: 16
11	Operation	operator: 31 operand: 24
12	Operation	operator: 31 operand: 25
13	Operation	operator: 22 operand: 29
14	ExprTuple	20
15	ExprTuple	21
16	Operation	operator: 22 operand: 26
17	ExprTuple	24
18	ExprTuple	25
19	ExprTuple	29
20	Variable
21	Variable
22	Variable
23	ExprTuple	26
24	Variable
25	Variable
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29, 30
29	Operation	operator: 31 operand: 33
30	Variable
31	Literal
32	ExprTuple	33
33	Variable