Expression of type ExprTuple

from the theory of proveit.physics.quantum.algebra

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, Conditional, ExprTuple, Lambda, U, n
from proveit.linear_algebra import Adj, MatrixSpace, Unitary
from proveit.logic import Equals, Exists, InSet
from proveit.numbers import Complex, sqrt
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(A, Conditional(Exists(instance_param_or_params = [U], instance_expr = Equals(A, Qmult(U, sqrt(Qmult(Adj(A), A)))), domain = Unitary(n)), InSet(A, MatrixSpace(field = Complex, rows = n, columns = n)))))

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\{\exists_{U \in \textrm{U}\left(n\right)}~\left(A = \left(U \thinspace \sqrt{\left(A^{\dagger} \thinspace A\right)}\right)\right) \textrm{ if } A \in \mathbb{C}^{n \times n}\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: 42 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	42, 9
8	Lambda	parameter: 26 body: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	26
11	Conditional	value: 14 condition: 15
12	Literal
13	NamedExprs	field: 16 rows: 28 columns: 28
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	42, 21
19	Literal
20	ExprTuple	26, 22
21	Operation	operator: 33 operands: 23
22	Operation	operator: 24 operand: 28
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28
26	Variable
27	Operation	operator: 29 operands: 30
28	Variable
29	Literal
30	ExprTuple	31, 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37, 42
35	Literal
36	ExprTuple	38, 39
37	Operation	operator: 40 operand: 42
38	Literal
39	Literal
40	Literal
41	ExprTuple	42
42	Variable