Expression of type Equals

from the theory of proveit.numbers.number_sets.complex_numbers

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 r, x
from proveit.logic import Equals
from proveit.numbers import Exp, Mod, Mult, Neg, e, frac, i, pi, two

# build up the expression from sub-expressions
expr = Equals(Exp(e, frac(Neg(Mult(two, pi, i, Mod(x, r))), r)), Exp(e, frac(Neg(Mult(two, pi, i, x)), r)))

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())

\mathsf{e}^{\frac{-\left(2 \cdot \pi \cdot \mathsf{i} \cdot \left(x ~\textup{mod}~ r\right)\right)}{r}} = \mathsf{e}^{\frac{-\left(2 \cdot \pi \cdot \mathsf{i} \cdot x\right)}{r}}

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