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, i, j
from proveit.core_expr_types import f_i_to_j
from proveit.logic import Equals
from proveit.numbers import Add, one, subtract

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

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(\left(i - 1\right) + 1\right), f\left(i + 1\right), \ldots, f\left(\left(j - 1\right) + 1\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: 18 end_index: 19
6	ExprRange	lambda_map: 8 start_index: 9 end_index: 10
7	Lambda	parameter: 26 body: 11
8	Lambda	parameter: 26 body: 12
9	Operation	operator: 24 operands: 13
10	Operation	operator: 24 operands: 14
11	Operation	operator: 16 operand: 26
12	Operation	operator: 16 operand: 21
13	ExprTuple	18, 20
14	ExprTuple	19, 20
15	ExprTuple	26
16	Variable
17	ExprTuple	21
18	Variable
19	Variable
20	Operation	operator: 22 operand: 27
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	27
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Literal