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 Hspace, LinMap
from proveit.logic import Forall, InSet
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(A, var_ket_psi), X), domain = Hspace), InSet(Qmult(A), LinMap(Hspace, X)))

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_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) \in X\right) \textrm{ if } \left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)\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: 17 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 25 body: 10
7	Operation	operator: 22 operand: 24
8	Operation	operator: 12 operands: 13
9	ExprTuple	25
10	Conditional	value: 14 condition: 15
11	ExprTuple	24
12	Literal
13	ExprTuple	21, 20
14	Operation	operator: 17 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	25, 21
19	Operation	operator: 22 operands: 23
20	Variable
21	Variable
22	Literal
23	ExprTuple	24, 25
24	Variable
25	Variable