Expression of type Equals

from the theory of proveit.numbers.summation

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 i, m, x
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Interval, Sum, one, zero

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Exp(x, i)
sub_expr3 = Add(m, one)
expr = Equals(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(zero, sub_expr3)), Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(zero, m)), Exp(x, sub_expr3)))

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(\sum_{i = 0}^{m + 1} x^{i}\right) = \left(\left(\sum_{i = 0}^{m} x^{i}\right) + x^{m + 1}\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	Operation	operator: 11 operand: 7
4	Operation	operator: 31 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 29 body: 10
8	Operation	operator: 11 operand: 15
9	Operation	operator: 23 operands: 13
10	Conditional	value: 20 condition: 14
11	Literal
12	ExprTuple	15
13	ExprTuple	28, 27
14	Operation	operator: 25 operands: 16
15	Lambda	parameter: 29 body: 18
16	ExprTuple	29, 19
17	ExprTuple	29
18	Conditional	value: 20 condition: 21
19	Operation	operator: 33 operands: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprTuple	36, 27
23	Literal
24	ExprTuple	28, 29
25	Literal
26	ExprTuple	29, 30
27	Operation	operator: 31 operands: 32
28	Variable
29	Variable
30	Operation	operator: 33 operands: 34
31	Literal
32	ExprTuple	37, 35
33	Literal
34	ExprTuple	36, 37
35	Literal
36	Literal
37	Variable