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, delta, 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 = Mult(two, pi, i, a)
sub_expr2 = Mult(two, pi, i, b)
sub_expr3 = Mult(Add(Mult(two, pi, i, delta), Mult(two, pi, i, theta)), k)
expr = Equals(Mult(Exp(e, sub_expr1), Exp(e, sub_expr3), Exp(e, sub_expr2)), Exp(e, Add(sub_expr1, sub_expr3, sub_expr2)))

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 a} \cdot \mathsf{e}^{\left(\left(2 \cdot \pi \cdot \mathsf{i} \cdot \delta\right) + \left(2 \cdot \pi \cdot \mathsf{i} \cdot \theta\right)\right) \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}\right) = \mathsf{e}^{\left(2 \cdot \pi \cdot \mathsf{i} \cdot a\right) + \left(\left(\left(2 \cdot \pi \cdot \mathsf{i} \cdot \delta\right) + \left(2 \cdot \pi \cdot \mathsf{i} \cdot \theta\right)\right) \cdot k\right) + \left(2 \cdot \pi \cdot \mathsf{i} \cdot b\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: 32 operands: 5
4	Operation	operator: 13 operands: 6
5	ExprTuple	7, 8, 9
6	ExprTuple	16, 10
7	Operation	operator: 13 operands: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 27 operands: 15
11	ExprTuple	16, 17
12	ExprTuple	16, 18
13	Literal
14	ExprTuple	16, 19
15	ExprTuple	17, 18, 19
16	Literal
17	Operation	operator: 32 operands: 20
18	Operation	operator: 32 operands: 21
19	Operation	operator: 32 operands: 22
20	ExprTuple	35, 36, 37, 23
21	ExprTuple	24, 25
22	ExprTuple	35, 36, 37, 26
23	Variable
24	Operation	operator: 27 operands: 28
25	Variable
26	Variable
27	Literal
28	ExprTuple	29, 30
29	Operation	operator: 32 operands: 31
30	Operation	operator: 32 operands: 33
31	ExprTuple	35, 36, 37, 34
32	Literal
33	ExprTuple	35, 36, 37, 38
34	Variable
35	Literal
36	Literal
37	Literal
38	Variable