Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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