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, Add, Mult, frac, pi, subtract, two

# build up the expression from sub-expressions
expr = Equals(frac(Abs(subtract(Add(Mult(two, pi, theta), pi), pi)), two), frac(Mult(two, pi, Abs(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())

\frac{\left|\left(\left(2 \cdot \pi \cdot \theta\right) + \pi\right) - \pi\right|}{2} = \frac{2 \cdot \pi \cdot \left|\theta\right|}{2}

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