Expression of type ExprTuple

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, ExprTuple, Lambda
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
sub_expr1 = [A, B]
expr = ExprTuple(Lambda(sub_expr1, 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 = sub_expr1), 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(\left(A, B\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 28 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 19 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 26 body: 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Conditional	value: 15 condition: 16
12	ExprTuple	33, 17
13	Literal
14	ExprTuple	35, 17
15	Operation	operator: 30 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 30 operands: 29
24	Operation	operator: 30 operands: 31
25	Literal
26	ExprTuple	32, 34
27	Literal
28	ExprTuple	33, 35
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34, 35
32	Variable
33	Variable
34	Variable
35	Variable