Expression of type Conditional

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, U
from proveit.linear_algebra import Adj, Hspace, Identity, LinMap
from proveit.logic import And, Equals, InSet
from proveit.numbers import sqrt

# build up the expression from sub-expressions
expr = Conditional(Equals(A, Composition(sqrt(Composition(A, Adj(A))), U)), And(InSet(U, LinMap(Hspace, Hspace)), Equals(Composition(Adj(U), U), Identity(Hspace))))

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 = \left(\sqrt{\left(A \circ A^{\dagger}\right)} \circ U\right) \textrm{ if } U \in \mathcal{L}\left(\mathcal{H}, \mathcal{H}\right) ,  \left(U^{\dagger} \circ U\right) = I_{\mathcal{H}}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 12 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	40, 6
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 29 operands: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	14, 37
10	Literal
11	ExprTuple	37, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Operation	operator: 29 operands: 22
17	Operation	operator: 23 operand: 28
18	Literal
19	ExprTuple	25, 26
20	Literal
21	ExprTuple	28, 28
22	ExprTuple	27, 37
23	Literal
24	ExprTuple	28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	Operation	operator: 38 operand: 37
28	Variable
29	Literal
30	ExprTuple	40, 34
31	Literal
32	ExprTuple	35, 36
33	ExprTuple	37
34	Operation	operator: 38 operand: 40
35	Literal
36	Literal
37	Variable
38	Literal
39	ExprTuple	40
40	Variable