Expression of type Conditional ¶

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

# build up the expression from sub-expressions
expr = Conditional(Equals(Abs(subtract(Exp(e, Mult(i, a)), Exp(e, Mult(i, b)))), Mult(two, Sin(frac(Abs(subtract(a, b)), two)))), And(InSet(a, Real), InSet(b, Real)))

# 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|\mathsf{e}^{\mathsf{i} \cdot a} - \mathsf{e}^{\mathsf{i} \cdot b}\right| = \left(2 \cdot \sin{\frac{\left|a - b\right|}{2}}\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 36 operand: 16
8	Operation	operator: 41 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	16
12	ExprTuple	32, 17
13	ExprTuple	46, 18
14	Literal
15	ExprTuple	50, 18
16	Operation	operator: 43 operands: 19
17	Operation	operator: 20 operand: 24
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24
22	Operation	operator: 34 operands: 25
23	Operation	operator: 48 operand: 30
24	Operation	operator: 27 operands: 28
25	ExprTuple	38, 29
26	ExprTuple	30
27	Literal
28	ExprTuple	31, 32
29	Operation	operator: 41 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 36 operand: 40
32	Literal
33	ExprTuple	45, 46
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40
38	Literal
39	Operation	operator: 41 operands: 42
40	Operation	operator: 43 operands: 44
41	Literal
42	ExprTuple	45, 50
43	Literal
44	ExprTuple	46, 47
45	Literal
46	Variable
47	Operation	operator: 48 operand: 50
48	Literal
49	ExprTuple	50
50	Variable

Expression of type Conditional¶

from the theory of proveit.trigonometry¶

Expression of type Conditional ¶

from the theory of proveit.trigonometry ¶