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 Exists, 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(Exists(instance_param_or_params = [Hspace, X, Y], instance_expr = InSet([Qmult(A), Qmult(B)], Set([sub_expr1, Hspace], [X, LinMap(Hspace, Complex)], [LinMap(X, Y), sub_expr1], [Complex, QmultCodomain], [QmultCodomain, Complex])), domain = HilbertSpaces), InClass(Qmult(A, B), QmultCodomain))

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\{\exists_{\mathcal{H}, X, Y \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\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\}\right) \textrm{ if } \left(A \thinspace B\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\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 operand: 6
2	Operation	operator: 28 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 44
6	Lambda	parameters: 8 body: 9
7	Operation	operator: 31 operands: 10
8	ExprTuple	51, 52, 50
9	Conditional	value: 11 condition: 12
10	ExprTuple	39, 40
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20, 21
17	ExprTuple	22, 23
18	Operation	operator: 24 operands: 25
19	Operation	operator: 28 operands: 26
20	Operation	operator: 28 operands: 27
21	Operation	operator: 28 operands: 29
22	Operation	operator: 31 operand: 39
23	Operation	operator: 31 operand: 40
24	Literal
25	ExprTuple	33, 34, 35, 36, 37
26	ExprTuple	51, 38
27	ExprTuple	52, 38
28	Literal
29	ExprTuple	50, 38
30	ExprTuple	39
31	Literal
32	ExprTuple	40
33	ExprTuple	43, 51
34	ExprTuple	52, 41
35	ExprTuple	42, 43
36	ExprTuple	49, 44
37	ExprTuple	44, 49
38	Literal
39	Variable
40	Variable
41	Operation	operator: 47 operands: 45
42	Operation	operator: 47 operands: 46
43	Operation	operator: 47 operands: 48
44	Literal
45	ExprTuple	51, 49
46	ExprTuple	52, 50
47	Literal
48	ExprTuple	51, 52
49	Literal
50	Variable
51	Variable
52	Variable