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 = Neg(r)
expr = Equals(Mult(sub_expr1, Exp(e, Mult(Neg(theta), i))), Mult(sub_expr1, Exp(e, Neg(Mult(theta, i)))))

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\right) \cdot \mathsf{i}}\right) = \left(\left(-r\right) \cdot \mathsf{e}^{-\left(\theta \cdot \mathsf{i}\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	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 12 operands: 10
8	Operation	operator: 22 operand: 15
9	Operation	operator: 12 operands: 13
10	ExprTuple	16, 14
11	ExprTuple	15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 24 operands: 18
15	Variable
16	Literal
17	Operation	operator: 22 operand: 21
18	ExprTuple	20, 27
19	ExprTuple	21
20	Operation	operator: 22 operand: 26
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Literal