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, B, Conditional
from proveit.linear_algebra import HilbertSpaces, TensorProd
from proveit.logic import And, Forall, InClass, InSet
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 = InSet(Qmult(var_ket_psi, var_ket_varphi), TensorProd(A, B)), domains = [A, B]), And(InClass(A, HilbertSpaces), InClass(B, 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 A, \lvert \varphi \rangle \in B}~\left(\left(\lvert \psi \rangle \thinspace \lvert \varphi \rangle\right) \in \left(A {\otimes} B\right)\right) \textrm{ if } A \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  B \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: 6
2	Operation	operator: 17 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 24 body: 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Conditional	value: 13 condition: 14
10	ExprTuple	31, 15
11	Literal
12	ExprTuple	33, 15
13	Operation	operator: 28 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operands: 26
21	Operation	operator: 28 operands: 27
22	Operation	operator: 28 operands: 29
23	Literal
24	ExprTuple	30, 32
25	Literal
26	ExprTuple	31, 33
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 33
30	Variable
31	Variable
32	Variable
33	Variable