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 Exists, InClass, InSet, Set
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = ExprTuple(Lambda([A, B], Conditional(Exists(instance_param_or_params = [Hspace, X, Y], instance_expr = InSet([Qmult(A), Qmult(B)], Set([sub_expr1, Hspace], [X, LinMap(Hspace, Complex)], [LinMap(X, Y), sub_expr1], [Complex, QmultCodomain], [QmultCodomain, Complex])), domain = HilbertSpaces), InClass(Qmult(A, B), QmultCodomain))))

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(A, B\right) \mapsto \left\{\exists_{\mathcal{H}, X, Y \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left(\left(\left[A\right], \left[B\right]\right) \in \left\{\left(\mathcal{L}\left(\mathcal{H}, X\right), \mathcal{H}\right), \left(X, \mathcal{L}\left(\mathcal{H}, \mathbb{C}\right)\right), \left(\mathcal{L}\left(X, Y\right), \mathcal{L}\left(\mathcal{H}, X\right)\right), \left(\mathbb{C}, \mathcal{Q^*}\right), \left(\mathcal{Q^*}, \mathbb{C}\right)\right\}\right) \textrm{ if } \left(A \thinspace B\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\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: 12 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 30 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 46
8	Lambda	parameters: 10 body: 11
9	Operation	operator: 33 operands: 12
10	ExprTuple	53, 54, 52
11	Conditional	value: 13 condition: 14
12	ExprTuple	41, 42
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22, 23
19	ExprTuple	24, 25
20	Operation	operator: 26 operands: 27
21	Operation	operator: 30 operands: 28
22	Operation	operator: 30 operands: 29
23	Operation	operator: 30 operands: 31
24	Operation	operator: 33 operand: 41
25	Operation	operator: 33 operand: 42
26	Literal
27	ExprTuple	35, 36, 37, 38, 39
28	ExprTuple	53, 40
29	ExprTuple	54, 40
30	Literal
31	ExprTuple	52, 40
32	ExprTuple	41
33	Literal
34	ExprTuple	42
35	ExprTuple	45, 53
36	ExprTuple	54, 43
37	ExprTuple	44, 45
38	ExprTuple	51, 46
39	ExprTuple	46, 51
40	Literal
41	Variable
42	Variable
43	Operation	operator: 49 operands: 47
44	Operation	operator: 49 operands: 48
45	Operation	operator: 49 operands: 50
46	Literal
47	ExprTuple	53, 51
48	ExprTuple	54, 52
49	Literal
50	ExprTuple	53, 54
51	Literal
52	Variable
53	Variable
54	Variable