Expression of type Equals

from the theory of proveit.numbers.absolute_value

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 r, theta
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, e, i

# build up the expression from sub-expressions
sub_expr1 = Exp(e, Neg(Mult(theta, i)))
expr = Equals(Mult(Neg(r), sub_expr1), Neg(Mult(r, sub_expr1)))

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(-r\right) \cdot \mathsf{e}^{-\left(\theta \cdot \mathsf{i}\right)}\right) = \left(-\left(r \cdot \mathsf{e}^{-\left(\theta \cdot \mathsf{i}\right)}\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: 20 operands: 5
4	Operation	operator: 17 operand: 8
5	ExprTuple	7, 12
6	ExprTuple	8
7	Operation	operator: 17 operand: 11
8	Operation	operator: 20 operands: 10
9	ExprTuple	11
10	ExprTuple	11, 12
11	Variable
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Literal
16	Operation	operator: 17 operand: 19
17	Literal
18	ExprTuple	19
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23
22	Variable
23	Literal