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 a, b, c, theta
from proveit.logic import Equals
from proveit.numbers import Abs, Exp, Mult, e, i, one

# build up the expression from sub-expressions
sub_expr1 = Abs(a)
expr = Equals(Mult(sub_expr1, Abs(b), Abs(Exp(e, Mult(i, theta))), Abs(c)), Mult(sub_expr1, b, one, c)).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|a\right| \cdot \left|b\right| \cdot \left|\mathsf{e}^{\mathsf{i} \cdot \theta}\right| \cdot \left|c\right|\right) =  \\ \left(\left|a\right| \cdot b \cdot 1 \cdot c\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: 25 operands: 5
4	Operation	operator: 25 operands: 6
5	ExprTuple	10, 7, 8, 9
6	ExprTuple	10, 17, 11, 19
7	Operation	operator: 15 operand: 17
8	Operation	operator: 15 operand: 18
9	Operation	operator: 15 operand: 19
10	Operation	operator: 15 operand: 20
11	Literal
12	ExprTuple	17
13	ExprTuple	18
14	ExprTuple	19
15	Literal
16	ExprTuple	20
17	Variable
18	Operation	operator: 21 operands: 22
19	Variable
20	Variable
21	Literal
22	ExprTuple	23, 24
23	Literal
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Variable