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 a, b, r
from proveit.logic import Equals
from proveit.numbers import Abs, Exp, Mult, e, frac, i, subtract, two
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
expr = Equals(Abs(subtract(Mult(r, Exp(e, Mult(i, a))), Mult(r, Exp(e, Mult(i, b))))), Mult(two, r, Sin(frac(Abs(subtract(a, b)), 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|\left(r \cdot \mathsf{e}^{\mathsf{i} \cdot a}\right) - \left(r \cdot \mathsf{e}^{\mathsf{i} \cdot b}\right)\right| = \left(2 \cdot r \cdot \sin{\frac{\left|a - b\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: 25 operand: 7
4	Operation	operator: 40 operands: 6
5	ExprTuple	7
6	ExprTuple	22, 28, 8
7	Operation	operator: 34 operands: 9
8	Operation	operator: 10 operand: 14
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14
12	Operation	operator: 40 operands: 15
13	Operation	operator: 42 operand: 20
14	Operation	operator: 17 operands: 18
15	ExprTuple	28, 19
16	ExprTuple	20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 32 operands: 23
20	Operation	operator: 40 operands: 24
21	Operation	operator: 25 operand: 30
22	Literal
23	ExprTuple	36, 27
24	ExprTuple	28, 29
25	Literal
26	ExprTuple	30
27	Operation	operator: 40 operands: 31
28	Variable
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	ExprTuple	44, 38
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38, 39
36	Literal
37	Operation	operator: 40 operands: 41
38	Variable
39	Operation	operator: 42 operand: 45
40	Literal
41	ExprTuple	44, 45
42	Literal
43	ExprTuple	45
44	Literal
45	Variable