Expression of type Equals

from the theory of proveit.trigonometry

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 theta
from proveit.logic import Equals
from proveit.numbers import Abs, Exp, Mult, e, frac, i, one, pi, subtract, two, zero
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
expr = Equals(Abs(subtract(one, Exp(e, Mult(two, pi, i, theta)))), Mult(two, Sin(frac(Abs(subtract(zero, Mult(two, pi, theta))), two))))

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|1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta}\right| = \left(2 \cdot \sin{\frac{\left|0 - \left(2 \cdot \pi \cdot \theta\right)\right|}{2}}\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: 22 operand: 7
4	Operation	operator: 36 operands: 6
5	ExprTuple	7
6	ExprTuple	38, 8
7	Operation	operator: 28 operands: 9
8	Operation	operator: 10 operand: 14
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14
12	Literal
13	Operation	operator: 33 operand: 18
14	Operation	operator: 16 operands: 17
15	ExprTuple	18
16	Literal
17	ExprTuple	19, 38
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operand: 26
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26
24	Literal
25	Operation	operator: 36 operands: 27
26	Operation	operator: 28 operands: 29
27	ExprTuple	38, 39, 30, 40
28	Literal
29	ExprTuple	31, 32
30	Literal
31	Literal
32	Operation	operator: 33 operand: 35
33	Literal
34	ExprTuple	35
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39, 40
38	Literal
39	Literal
40	Variable