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 Equals, Forall, InSet
from proveit.numbers import Abs, Exp, Mult, Real, RealNonNeg, e, frac, i, subtract, two
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(r, Conditional(Forall(instance_param_or_params = [a, b], instance_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)))), domain = Real), InSet(r, RealNonNeg))))

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(r \mapsto \left\{\forall_{a, b \in \mathbb{R}}~\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)\right) \textrm{ if } r \in \mathbb{R}^{\ge 0}\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	parameter: 50 body: 3
2	ExprTuple	50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 26 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	50, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	60, 67
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 47 operand: 28
20	Operation	operator: 62 operands: 24
21	Operation	operator: 26 operands: 25
22	Operation	operator: 26 operands: 27
23	ExprTuple	28
24	ExprTuple	44, 50, 29
25	ExprTuple	60, 30
26	Literal
27	ExprTuple	67, 30
28	Operation	operator: 56 operands: 31
29	Operation	operator: 32 operand: 36
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36
34	Operation	operator: 62 operands: 37
35	Operation	operator: 64 operand: 42
36	Operation	operator: 39 operands: 40
37	ExprTuple	50, 41
38	ExprTuple	42
39	Literal
40	ExprTuple	43, 44
41	Operation	operator: 54 operands: 45
42	Operation	operator: 62 operands: 46
43	Operation	operator: 47 operand: 52
44	Literal
45	ExprTuple	58, 49
46	ExprTuple	50, 51
47	Literal
48	ExprTuple	52
49	Operation	operator: 62 operands: 53
50	Variable
51	Operation	operator: 54 operands: 55
52	Operation	operator: 56 operands: 57
53	ExprTuple	66, 60
54	Literal
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	60, 61
58	Literal
59	Operation	operator: 62 operands: 63
60	Variable
61	Operation	operator: 64 operand: 67
62	Literal
63	ExprTuple	66, 67
64	Literal
65	ExprTuple	67
66	Literal
67	Variable