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 ExprRange, Variable, k, m
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Sum, one, subtract, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(m, one)
expr = Equals(Len(operands = [Sum(index_or_indices = [k], summand = k, domain = Interval(one, subtract(sub_expr2, one))), sub_expr2]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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_{k = 1}^{\left(m + 1\right) - 1} k, m + 1\right)| = |\left(1, \ldots, 2\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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 28
6	Literal
7	ExprTuple	9
8	Operation	operator: 10 operand: 14
9	ExprRange	lambda_map: 12 start_index: 35 end_index: 13
10	Literal
11	ExprTuple	14
12	Lambda	parameter: 18 body: 18
13	Literal
14	Lambda	parameter: 22 body: 17
15	ExprTuple	18
16	ExprTuple	22
17	Conditional	value: 22 condition: 19
18	Variable
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23
22	Variable
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	35, 26
26	Operation	operator: 30 operands: 27
27	ExprTuple	28, 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operand: 35
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	35
34	Variable
35	Literal