Expression of type Lambda

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, Lambda, 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 = Lambda([a, b], 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))))

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(a, b\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	48, 52
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 38 operand: 18
10	Operation	operator: 43 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18
14	ExprTuple	34, 19
15	ExprTuple	48, 20
16	Literal
17	ExprTuple	52, 20
18	Operation	operator: 45 operands: 21
19	Operation	operator: 22 operand: 26
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26
24	Operation	operator: 36 operands: 27
25	Operation	operator: 50 operand: 32
26	Operation	operator: 29 operands: 30
27	ExprTuple	40, 31
28	ExprTuple	32
29	Literal
30	ExprTuple	33, 34
31	Operation	operator: 43 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operand: 42
34	Literal
35	ExprTuple	47, 48
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42
40	Literal
41	Operation	operator: 43 operands: 44
42	Operation	operator: 45 operands: 46
43	Literal
44	ExprTuple	47, 52
45	Literal
46	ExprTuple	48, 49
47	Literal
48	Variable
49	Operation	operator: 50 operand: 52
50	Literal
51	ExprTuple	52
52	Variable