Expression of type ExprTuple

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, ExprTuple, Lambda, a, b, r
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 = ExprTuple(Lambda([a, b], Conditional(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)))), 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(\left(a, b\right) \mapsto \left\{\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) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	51, 58
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13
10	Operation	operator: 38 operand: 19
11	Operation	operator: 53 operands: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	19
15	ExprTuple	35, 41, 20
16	ExprTuple	51, 21
17	Literal
18	ExprTuple	58, 21
19	Operation	operator: 47 operands: 22
20	Operation	operator: 23 operand: 27
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27
25	Operation	operator: 53 operands: 28
26	Operation	operator: 55 operand: 33
27	Operation	operator: 30 operands: 31
28	ExprTuple	41, 32
29	ExprTuple	33
30	Literal
31	ExprTuple	34, 35
32	Operation	operator: 45 operands: 36
33	Operation	operator: 53 operands: 37
34	Operation	operator: 38 operand: 43
35	Literal
36	ExprTuple	49, 40
37	ExprTuple	41, 42
38	Literal
39	ExprTuple	43
40	Operation	operator: 53 operands: 44
41	Variable
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 48
44	ExprTuple	57, 51
45	Literal
46	ExprTuple	49, 50
47	Literal
48	ExprTuple	51, 52
49	Literal
50	Operation	operator: 53 operands: 54
51	Variable
52	Operation	operator: 55 operand: 58
53	Literal
54	ExprTuple	57, 58
55	Literal
56	ExprTuple	58
57	Literal
58	Variable