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

# build up the expression from sub-expressions
sub_expr1 = Exp(Exp(e, Mult(two, pi, i, delta)), k)
expr = Equals(Mult(sub_expr1, Exp(e, Mult(two, pi, i, theta, k))), Mult(sub_expr1, Exp(Exp(e, Mult(two, pi, i, theta)), k)))

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((\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \delta})^{k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta \cdot k}\right) = \left((\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \delta})^{k} \cdot (\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta})^{k}\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: 25 operands: 5
4	Operation	operator: 25 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 18 operands: 10
8	Operation	operator: 18 operands: 11
9	Operation	operator: 18 operands: 12
10	ExprTuple	22, 13
11	ExprTuple	14, 20
12	ExprTuple	15, 20
13	Operation	operator: 25 operands: 16
14	Operation	operator: 18 operands: 17
15	Operation	operator: 18 operands: 19
16	ExprTuple	28, 29, 30, 31, 20
17	ExprTuple	22, 21
18	Literal
19	ExprTuple	22, 23
20	Variable
21	Operation	operator: 25 operands: 24
22	Literal
23	Operation	operator: 25 operands: 26
24	ExprTuple	28, 29, 30, 27
25	Literal
26	ExprTuple	28, 29, 30, 31
27	Variable
28	Literal
29	Literal
30	Literal
31	Variable