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
expr = Equals(Mult(Exp(e, Mult(two, pi, i, k, delta)), Exp(e, Mult(two, pi, i, theta, k))), Exp(Mult(Exp(e, Mult(two, pi, i, delta)), 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 k \cdot \delta} \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} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta}\right)^{k}

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: 27 operands: 5
4	Operation	operator: 20 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 22
7	Operation	operator: 20 operands: 10
8	Operation	operator: 20 operands: 11
9	Operation	operator: 27 operands: 12
10	ExprTuple	24, 13
11	ExprTuple	24, 14
12	ExprTuple	15, 16
13	Operation	operator: 27 operands: 17
14	Operation	operator: 27 operands: 18
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	ExprTuple	30, 31, 32, 22, 29
18	ExprTuple	30, 31, 32, 33, 22
19	ExprTuple	24, 23
20	Literal
21	ExprTuple	24, 25
22	Variable
23	Operation	operator: 27 operands: 26
24	Literal
25	Operation	operator: 27 operands: 28
26	ExprTuple	30, 31, 32, 29
27	Literal
28	ExprTuple	30, 31, 32, 33
29	Variable
30	Literal
31	Literal
32	Literal
33	Variable