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, Hspace, Identity, LinMap
from proveit.logic import Equals, Exists, InSet
from proveit.numbers import sqrt

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, Hspace)
expr = ExprTuple(Lambda(A, Conditional(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(), InSet(A, sub_expr1))))

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 \mapsto \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} \textrm{ if } A \in \mathcal{L}\left(\mathcal{H}, \mathcal{H}\right)\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: 49 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 19 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	49, 24
8	Lambda	parameter: 46 body: 9
9	Conditional	value: 10 condition: 11
10	Operation	operator: 21 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	49, 15
13	Literal
14	ExprTuple	16, 17
15	Operation	operator: 38 operands: 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	23, 46
19	Literal
20	ExprTuple	46, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 38 operands: 31
26	Operation	operator: 32 operand: 37
27	Literal
28	ExprTuple	34, 35
29	Literal
30	ExprTuple	37, 37
31	ExprTuple	36, 46
32	Literal
33	ExprTuple	37
34	Operation	operator: 38 operands: 39
35	Operation	operator: 40 operands: 41
36	Operation	operator: 47 operand: 46
37	Variable
38	Literal
39	ExprTuple	49, 43
40	Literal
41	ExprTuple	44, 45
42	ExprTuple	46
43	Operation	operator: 47 operand: 49
44	Literal
45	Literal
46	Variable
47	Literal
48	ExprTuple	49
49	Variable