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, 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([Hspace, X, Y], Conditional(InSet([Qmult(A), Qmult(B)], Set([sub_expr1, Hspace], [X, LinMap(Hspace, Complex)], [LinMap(X, Y), sub_expr1], [Complex, QmultCodomain], [QmultCodomain, Complex])), 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\{\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\} \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	44, 45, 43
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	ExprTuple	15, 16
11	Operation	operator: 17 operands: 18
12	Operation	operator: 21 operands: 19
13	Operation	operator: 21 operands: 20
14	Operation	operator: 21 operands: 22
15	Operation	operator: 24 operand: 32
16	Operation	operator: 24 operand: 33
17	Literal
18	ExprTuple	26, 27, 28, 29, 30
19	ExprTuple	44, 31
20	ExprTuple	45, 31
21	Literal
22	ExprTuple	43, 31
23	ExprTuple	32
24	Literal
25	ExprTuple	33
26	ExprTuple	36, 44
27	ExprTuple	45, 34
28	ExprTuple	35, 36
29	ExprTuple	42, 37
30	ExprTuple	37, 42
31	Literal
32	Variable
33	Variable
34	Operation	operator: 40 operands: 38
35	Operation	operator: 40 operands: 39
36	Operation	operator: 40 operands: 41
37	Literal
38	ExprTuple	44, 42
39	ExprTuple	45, 43
40	Literal
41	ExprTuple	44, 45
42	Literal
43	Variable
44	Variable
45	Variable