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, X, Y
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import And, Forall, InClass, InSet
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([Hspace, X, Y], Conditional(Forall(instance_param_or_params = [A, B], instance_expr = InClass(Qmult(A, B), QmultCodomain), conditions = [InSet(Qmult(A), LinMap(X, Y)), InSet(Qmult(B), LinMap(Hspace, X))]), And(InClass(Hspace, HilbertSpaces), InClass(X, HilbertSpaces), InClass(Y, 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, Y\right) \mapsto \left\{\forall_{A, B~|~\left[A\right] \in \mathcal{L}\left(X, Y\right), \left[B\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left(\left(A \thinspace B\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  Y \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: 2 body: 3
2	ExprTuple	45, 46, 43
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 22 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 28 body: 13
10	Operation	operator: 20 operands: 14
11	Operation	operator: 20 operands: 15
12	Operation	operator: 20 operands: 16
13	Conditional	value: 17 condition: 18
14	ExprTuple	45, 19
15	ExprTuple	46, 19
16	ExprTuple	43, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 38 operands: 28
25	Literal
26	Operation	operator: 30 operands: 29
27	Operation	operator: 30 operands: 31
28	ExprTuple	42, 44
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34, 35
32	Operation	operator: 38 operand: 42
33	Operation	operator: 40 operands: 37
34	Operation	operator: 38 operand: 44
35	Operation	operator: 40 operands: 41
36	ExprTuple	42
37	ExprTuple	46, 43
38	Literal
39	ExprTuple	44
40	Literal
41	ExprTuple	45, 46
42	Variable
43	Variable
44	Variable
45	Variable
46	Variable