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 = Add(a, b)
sub_expr3 = Exp(e, Mult(two, pi, i, b))
expr = Equals(Mult(sub_expr1, Exp(e, Mult(two, pi, i, theta, k)), Exp(sub_expr2, k), sub_expr3), Mult(sub_expr1, Exp(Mult(Exp(e, Mult(two, pi, i, theta)), sub_expr2), k), sub_expr3)).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 \left(a + b\right)\right)^{k} \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: 34 operands: 5
4	Operation	operator: 34 operands: 6
5	ExprTuple	9, 7, 8, 11
6	ExprTuple	9, 10, 11
7	Operation	operator: 26 operands: 12
8	Operation	operator: 26 operands: 13
9	Operation	operator: 26 operands: 14
10	Operation	operator: 26 operands: 15
11	Operation	operator: 26 operands: 16
12	ExprTuple	30, 17
13	ExprTuple	25, 23
14	ExprTuple	32, 23
15	ExprTuple	18, 23
16	ExprTuple	30, 19
17	Operation	operator: 34 operands: 20
18	Operation	operator: 34 operands: 21
19	Operation	operator: 34 operands: 22
20	ExprTuple	36, 37, 38, 39, 23
21	ExprTuple	24, 25
22	ExprTuple	36, 37, 38, 33
23	Variable
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 33
30	Literal
31	Operation	operator: 34 operands: 35
32	Variable
33	Variable
34	Literal
35	ExprTuple	36, 37, 38, 39
36	Literal
37	Literal
38	Literal
39	Variable