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 Conditional, ExprTuple, Lambda
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 = ExprTuple(Lambda(Hspace, 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(\mathcal{H} \mapsto \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..\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	parameter: 31 body: 3
2	ExprTuple	31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	31, 11
10	Lambda	parameters: 25 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 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: 25
20	Operation	operator: 24 operands: 25
21	Operation	operator: 27 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	Literal
25	ExprTuple	29, 30
26	ExprTuple	29, 31
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Variable