Expression of type ExprTuple

from the theory of proveit.linear_algebra.inner_products

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, Composition, Conditional, ExprTuple, Lambda, U
from proveit.linear_algebra import Adj, HilbertSpaces, Hspace, Identity, LinMap
from proveit.logic import Equals, Exists, Forall, InClass
from proveit.numbers import sqrt

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, Hspace)
expr = ExprTuple(Lambda(Hspace, Conditional(Forall(instance_param_or_params = [A], instance_expr = Exists(instance_param_or_params = [U], instance_expr = Equals(A, Composition(sqrt(Composition(A, Adj(A))), U)), domain = sub_expr1, condition = Equals(Composition(Adj(U), U), Identity(Hspace))).with_wrapping(), domain = sub_expr1), InClass(Hspace, HilbertSpaces))))

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(\mathcal{H} \mapsto \left\{\forall_{A \in \mathcal{L}\left(\mathcal{H}, \mathcal{H}\right)}~\left[\begin{array}{l}\exists_{U \in \mathcal{L}\left(\mathcal{H}, \mathcal{H}\right)~|~\left(U^{\dagger} \circ U\right) = I_{\mathcal{H}}}~\\
\left(A = \left(\sqrt{\left(A \circ A^{\dagger}\right)} \circ U\right)\right)\end{array}\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\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: 46 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	46, 10
9	Lambda	parameter: 58 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 17
13	Operation	operator: 28 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	58, 33
17	Lambda	parameter: 55 body: 18
18	Conditional	value: 19 condition: 20
19	Operation	operator: 30 operands: 21
20	Operation	operator: 22 operands: 23
21	ExprTuple	58, 24
22	Literal
23	ExprTuple	25, 26
24	Operation	operator: 47 operands: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	ExprTuple	32, 55
28	Literal
29	ExprTuple	55, 33
30	Literal
31	ExprTuple	34, 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operands: 39
34	Operation	operator: 47 operands: 40
35	Operation	operator: 41 operand: 46
36	Literal
37	ExprTuple	43, 44
38	Literal
39	ExprTuple	46, 46
40	ExprTuple	45, 55
41	Literal
42	ExprTuple	46
43	Operation	operator: 47 operands: 48
44	Operation	operator: 49 operands: 50
45	Operation	operator: 56 operand: 55
46	Variable
47	Literal
48	ExprTuple	58, 52
49	Literal
50	ExprTuple	53, 54
51	ExprTuple	55
52	Operation	operator: 56 operand: 58
53	Literal
54	Literal
55	Variable
56	Literal
57	ExprTuple	58
58	Variable