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

# build up the expression from sub-expressions
sub_expr1 = [var_ket_psi]
sub_expr2 = Qmult(A)
expr = ExprTuple(Lambda([Hspace, X], Conditional(Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Qmult(A, var_ket_psi), Function(sub_expr2, sub_expr1)), domain = Hspace), condition = InSet(sub_expr2, 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) = \left[A\right]\left(\lvert \psi \rangle\right)\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: 25 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: 42 body: 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Conditional	value: 15 condition: 16
12	ExprTuple	35, 17
13	Literal
14	ExprTuple	28, 17
15	Operation	operator: 18 operand: 21
16	Operation	operator: 31 operands: 20
17	Literal
18	Literal
19	ExprTuple	21
20	ExprTuple	37, 22
21	Lambda	parameter: 41 body: 23
22	Operation	operator: 24 operands: 25
23	Conditional	value: 26 condition: 27
24	Literal
25	ExprTuple	35, 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Variable
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	41, 35
33	Operation	operator: 39 operands: 36
34	Operation	operator: 37 operand: 41
35	Variable
36	ExprTuple	42, 41
37	Operation	operator: 39 operand: 42
38	ExprTuple	41
39	Literal
40	ExprTuple	42
41	Variable
42	Variable