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
from proveit.linear_algebra import HilbertSpaces, Hspace, TensorProd
from proveit.logic import Equals, Forall, InClass
from proveit.physics.quantum import Qmult, var_ket_psi, var_ket_varphi

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [var_ket_psi, var_ket_varphi], instance_expr = Equals(Qmult(var_ket_psi, var_ket_varphi), TensorProd(var_ket_psi, var_ket_varphi)), 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, \lvert \varphi \rangle \in \mathcal{H}}~\left(\left(\lvert \psi \rangle \thinspace \lvert \varphi \rangle\right) = \left(\lvert \psi \rangle {\otimes} \lvert \varphi \rangle\right)\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	28, 8
7	Lambda	parameters: 22 body: 9
8	Literal
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 20 operands: 22
17	Operation	operator: 21 operands: 22
18	Operation	operator: 24 operands: 23
19	Operation	operator: 24 operands: 25
20	Literal
21	Literal
22	ExprTuple	26, 27
23	ExprTuple	26, 28
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Variable