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 Conditional, c
from proveit.linear_algebra import HilbertSpaces, Hspace
from proveit.logic import Forall, InClass, 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(c, var_ket_psi), Hspace), domain = Hspace), InClass(Hspace, 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_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(c \thinspace \lvert \psi \rangle\right) \in \mathcal{H}\right) \textrm{ if } \mathcal{H} \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 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	17, 8
7	Lambda	parameter: 21 body: 10
8	Literal
9	ExprTuple	21
10	Conditional	value: 11 condition: 12
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	21, 17
16	Operation	operator: 18 operands: 19
17	Variable
18	Literal
19	ExprTuple	20, 21
20	Variable
21	Variable