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, Conditional, ExprTuple, Lambda, X
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import And, Forall, InClass, InSet
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([Hspace, X], Conditional(Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(A, var_ket_psi), X), domain = Hspace), condition = InSet(Qmult(A), LinMap(Hspace, X))), And(InClass(Hspace, HilbertSpaces), InClass(X, 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(\mathcal{H}, X\right) \mapsto \left\{\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) \in X\right)\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \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: 18 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	9, 10
8	Lambda	parameter: 39 body: 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Conditional	value: 15 condition: 16
12	ExprTuple	36, 17
13	Literal
14	ExprTuple	35, 17
15	Operation	operator: 18 operand: 21
16	Operation	operator: 32 operands: 20
17	Literal
18	Literal
19	ExprTuple	21
20	ExprTuple	22, 23
21	Lambda	parameter: 40 body: 25
22	Operation	operator: 37 operand: 39
23	Operation	operator: 27 operands: 28
24	ExprTuple	40
25	Conditional	value: 29 condition: 30
26	ExprTuple	39
27	Literal
28	ExprTuple	36, 35
29	Operation	operator: 32 operands: 31
30	Operation	operator: 32 operands: 33
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	40, 36
34	Operation	operator: 37 operands: 38
35	Variable
36	Variable
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Variable