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, Conditional, X
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import And, Forall, InClass, InSet
from proveit.physics.quantum import Qmult, QmultCodomain, var_ket_psi

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InClass(Qmult(A, var_ket_psi), QmultCodomain), domain = Hspace), condition = InSet(Qmult(A), LinMap(Hspace, X))), And(InClass(Hspace, HilbertSpaces), InClass(X, 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\{\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right)\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \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: 15 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	7, 8
6	Lambda	parameter: 38 body: 9
7	Operation	operator: 29 operands: 10
8	Operation	operator: 29 operands: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	35, 14
11	ExprTuple	28, 14
12	Operation	operator: 15 operand: 18
13	Operation	operator: 31 operands: 17
14	Literal
15	Literal
16	ExprTuple	18
17	ExprTuple	19, 20
18	Lambda	parameter: 39 body: 22
19	Operation	operator: 36 operand: 38
20	Operation	operator: 24 operands: 25
21	ExprTuple	39
22	Conditional	value: 26 condition: 27
23	ExprTuple	38
24	Literal
25	ExprTuple	35, 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Variable
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	39, 35
33	Operation	operator: 36 operands: 37
34	Literal
35	Variable
36	Literal
37	ExprTuple	38, 39
38	Variable
39	Variable