Expression of type Equals

from the theory of proveit.numbers.addition

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, IndexedVar, Variable, a, b, d, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals
from proveit.numbers import Add, frac, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Add(frac(a, d), frac(b, d), ExprRange(sub_expr1, frac(IndexedVar(a, sub_expr1), d), one, n)), frac(Add(a, b, a_1_to_n), d))

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(\frac{a}{d} + \frac{b}{d}+ \frac{a_{1}}{d} +  \frac{a_{2}}{d} +  \ldots +  \frac{a_{n}}{d}\right) = \frac{a + b+ a_{1} +  a_{2} +  \ldots +  a_{n}}{d}

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	Operation	operator: 14 operands: 5
4	Operation	operator: 19 operands: 6
5	ExprTuple	7, 8, 9
6	ExprTuple	10, 24
7	Operation	operator: 19 operands: 11
8	Operation	operator: 19 operands: 12
9	ExprRange	lambda_map: 13 start_index: 22 end_index: 23
10	Operation	operator: 14 operands: 15
11	ExprTuple	26, 24
12	ExprTuple	17, 24
13	Lambda	parameter: 28 body: 16
14	Literal
15	ExprTuple	26, 17, 18
16	Operation	operator: 19 operands: 20
17	Variable
18	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
19	Literal
20	ExprTuple	25, 24
21	Lambda	parameter: 28 body: 25
22	Literal
23	Variable
24	Variable
25	IndexedVar	variable: 26 index: 28
26	Variable
27	ExprTuple	28
28	Variable