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, c, m
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals
from proveit.numbers import Add, Neg, one, subtract

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Neg(c)
sub_expr3 = ExprRange(sub_expr1, Neg(IndexedVar(a, sub_expr1)), one, m)
sub_expr4 = Add(a_1_to_n)
expr = Equals(Add(Add(sub_expr3, b), subtract(sub_expr2, sub_expr4)), Add(sub_expr3, b, sub_expr2, Neg(sub_expr4)))

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(\left(- a_{1} -  a_{2} -  \ldots -  a_{m} + b\right) + \left(-c - \left(a_{1} +  a_{2} +  \ldots +  a_{n}\right)\right)\right) = \left(- a_{1} -  a_{2} -  \ldots -  a_{m} + b - c - \left(a_{1} +  a_{2} +  \ldots +  a_{n}\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	Operation	operator: 24 operands: 5
4	Operation	operator: 24 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	11, 12, 13, 14
7	Operation	operator: 24 operands: 9
8	Operation	operator: 24 operands: 10
9	ExprTuple	11, 12
10	ExprTuple	13, 14
11	ExprRange	lambda_map: 15 start_index: 28 end_index: 16
12	Variable
13	Operation	operator: 22 operand: 20
14	Operation	operator: 22 operand: 21
15	Lambda	parameter: 33 body: 19
16	Variable
17	ExprTuple	20
18	ExprTuple	21
19	Operation	operator: 22 operand: 30
20	Variable
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	30
24	Literal
25	ExprTuple	26
26	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
27	Lambda	parameter: 33 body: 30
28	Literal
29	Variable
30	IndexedVar	variable: 31 index: 33
31	Variable
32	ExprTuple	33
33	Variable