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, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, var_ket_psi

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

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_{\mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(\lvert \psi \rangle \thinspace c\right) \in \mathcal{H}\right)\right] \textrm{ if } c \in \mathbb{C}\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: 11 operand: 5
2	Operation	operator: 22 operands: 4
3	ExprTuple	5
4	ExprTuple	29, 6
5	Lambda	parameter: 25 body: 8
6	Literal
7	ExprTuple	25
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operand: 15
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	25, 16
15	Lambda	parameter: 28 body: 18
16	Literal
17	ExprTuple	28
18	Conditional	value: 19 condition: 20
19	Operation	operator: 22 operands: 21
20	Operation	operator: 22 operands: 23
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	28, 25
24	Operation	operator: 26 operands: 27
25	Variable
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Variable