Expression of type Conditional

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, B, Conditional, X, Y
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import And, InClass, InSet, Set
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Conditional(InSet([Qmult(A), Qmult(B)], Set([sub_expr1, Hspace], [X, LinMap(Hspace, Complex)], [LinMap(X, Y), sub_expr1], [Complex, QmultCodomain], [QmultCodomain, Complex])), And(InClass(Hspace, HilbertSpaces), InClass(X, HilbertSpaces), InClass(Y, 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\{\left(\left[A\right], \left[B\right]\right) \in \left\{\left(\mathcal{L}\left(\mathcal{H}, X\right), \mathcal{H}\right), \left(X, \mathcal{L}\left(\mathcal{H}, \mathbb{C}\right)\right), \left(\mathcal{L}\left(X, Y\right), \mathcal{L}\left(\mathcal{H}, X\right)\right), \left(\mathbb{C}, \mathcal{Q^*}\right), \left(\mathcal{Q^*}, \mathbb{C}\right)\right\} \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  Y \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	ExprTuple	12, 13
8	Operation	operator: 14 operands: 15
9	Operation	operator: 18 operands: 16
10	Operation	operator: 18 operands: 17
11	Operation	operator: 18 operands: 19
12	Operation	operator: 21 operand: 29
13	Operation	operator: 21 operand: 30
14	Literal
15	ExprTuple	23, 24, 25, 26, 27
16	ExprTuple	41, 28
17	ExprTuple	42, 28
18	Literal
19	ExprTuple	40, 28
20	ExprTuple	29
21	Literal
22	ExprTuple	30
23	ExprTuple	33, 41
24	ExprTuple	42, 31
25	ExprTuple	32, 33
26	ExprTuple	39, 34
27	ExprTuple	34, 39
28	Literal
29	Variable
30	Variable
31	Operation	operator: 37 operands: 35
32	Operation	operator: 37 operands: 36
33	Operation	operator: 37 operands: 38
34	Literal
35	ExprTuple	41, 39
36	ExprTuple	42, 40
37	Literal
38	ExprTuple	41, 42
39	Literal
40	Variable
41	Variable
42	Variable