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 Abs, Exp, Mult, Neg, e, i, one

# build up the expression from sub-expressions
expr = Equals(Mult(Abs(r), Abs(Exp(e, Neg(Mult(theta, i))))), Mult(r, one)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(\left|r\right| \cdot \left|\mathsf{e}^{-\left(\theta \cdot \mathsf{i}\right)}\right|\right) =  \\ \left(r \cdot 1\right) \end{array} \end{array}

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.	()	(2)	('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: 22 operands: 5
4	Operation	operator: 22 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	13, 9
7	Operation	operator: 11 operand: 13
8	Operation	operator: 11 operand: 14
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	14
13	Variable
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	17, 18
17	Literal
18	Operation	operator: 19 operand: 21
19	Literal
20	ExprTuple	21
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Variable
25	Literal