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 And, Equals, InSet
from proveit.numbers import sqrt

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(U, Conditional(Equals(A, Composition(U, sqrt(Composition(Adj(A), A)))), 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(U \mapsto \left\{A = \left(U \circ \sqrt{\left(A^{\dagger} \circ A\right)}\right) \textrm{ if } U \in \mathcal{L}\left(\mathcal{H}, \mathcal{H}\right) ,  \left(U^{\dagger} \circ U\right) = I_{\mathcal{H}}\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: 39 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 14 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	42, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 31 operands: 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	39, 16
12	Literal
13	ExprTuple	39, 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Operation	operator: 31 operands: 24
19	Operation	operator: 25 operand: 30
20	Literal
21	ExprTuple	27, 28
22	Literal
23	ExprTuple	30, 30
24	ExprTuple	29, 39
25	Literal
26	ExprTuple	30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	Operation	operator: 40 operand: 39
30	Variable
31	Literal
32	ExprTuple	36, 42
33	Literal
34	ExprTuple	37, 38
35	ExprTuple	39
36	Operation	operator: 40 operand: 42
37	Literal
38	Literal
39	Variable
40	Literal
41	ExprTuple	42
42	Variable