Expression of type Equals

from the theory of proveit.numbers.multiplication

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, k, theta
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, e, i, pi, two

# build up the expression from sub-expressions
sub_expr1 = Exp(a, k)
sub_expr2 = Exp(e, Mult(two, pi, i, theta, k))
sub_expr3 = Exp(Add(a, b), k)
sub_expr4 = Exp(e, Mult(two, pi, i, b))
expr = Equals(Mult(sub_expr1, sub_expr2, sub_expr3, sub_expr4), Mult(sub_expr1, Mult(sub_expr2, sub_expr3), sub_expr4)).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(a^{k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta \cdot k} \cdot \left(a + b\right)^{k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}\right) =  \\ \left(a^{k} \cdot \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta \cdot k} \cdot \left(a + b\right)^{k}\right) \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}\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: 23 operands: 5
4	Operation	operator: 23 operands: 6
5	ExprTuple	7, 13, 14, 9
6	ExprTuple	7, 8, 9
7	Operation	operator: 17 operands: 10
8	Operation	operator: 23 operands: 11
9	Operation	operator: 17 operands: 12
10	ExprTuple	32, 31
11	ExprTuple	13, 14
12	ExprTuple	20, 15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 23 operands: 19
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	22, 31
19	ExprTuple	27, 28, 29, 33
20	Literal
21	Operation	operator: 23 operands: 24
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	27, 28, 29, 30, 31
25	Literal
26	ExprTuple	32, 33
27	Literal
28	Literal
29	Literal
30	Variable
31	Variable
32	Variable
33	Variable