Expression of type Equals

from the theory of proveit.numbers.addition.subtraction

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 b, d
from proveit.core_expr_types import a_1_to_i, c_1_to_j, e_1_to_k
from proveit.logic import Equals
from proveit.numbers import Add, Neg

# build up the expression from sub-expressions
expr = Equals(Add(a_1_to_i, b, c_1_to_j, Neg(d), e_1_to_k), Add(a_1_to_i, c_1_to_j, e_1_to_k))

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(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j} - d+ e_{1} +  e_{2} +  \ldots +  e_{k}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ c_{1} +  c_{2} +  \ldots +  c_{j}+ e_{1} +  e_{2} +  \ldots +  e_{k}\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	10, 8, 11, 9, 12
6	Literal
7	ExprTuple	10, 11, 12
8	Variable
9	Operation	operator: 13 operand: 22
10	ExprRange	lambda_map: 15 start_index: 20 end_index: 16
11	ExprRange	lambda_map: 17 start_index: 20 end_index: 18
12	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
13	Literal
14	ExprTuple	22
15	Lambda	parameter: 30 body: 23
16	Variable
17	Lambda	parameter: 30 body: 24
18	Variable
19	Lambda	parameter: 30 body: 25
20	Literal
21	Variable
22	Variable
23	IndexedVar	variable: 26 index: 30
24	IndexedVar	variable: 27 index: 30
25	IndexedVar	variable: 28 index: 30
26	Variable
27	Variable
28	Variable
29	ExprTuple	30
30	Variable