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, Function, X
from proveit.linear_algebra import Hspace, LinMap
from proveit.logic import Equals, Forall, InSet
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
sub_expr1 = [var_ket_psi]
sub_expr2 = Qmult(A)
expr = Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qmult(A, var_ket_psi), Function(sub_expr2, sub_expr1)), domain = Hspace), InSet(sub_expr2, 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) = \left[A\right]\left(\lvert \psi \rangle\right)\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: 16 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	22, 7
6	Lambda	parameter: 26 body: 8
7	Operation	operator: 9 operands: 10
8	Conditional	value: 11 condition: 12
9	Literal
10	ExprTuple	20, 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Variable
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	26, 20
18	Operation	operator: 24 operands: 21
19	Operation	operator: 22 operand: 26
20	Variable
21	ExprTuple	27, 26
22	Operation	operator: 24 operand: 27
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Variable
27	Variable