Expression of type InSet

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, X, Y
from proveit.linear_algebra import Hspace, LinMap
from proveit.logic import 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 = InSet([Qmult(A), Qmult(B)], Set([sub_expr1, Hspace], [X, LinMap(Hspace, Complex)], [LinMap(X, Y), sub_expr1], [Complex, QmultCodomain], [QmultCodomain, Complex]))

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\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\}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	ExprTuple	5, 6
4	Operation	operator: 7 operands: 8
5	Operation	operator: 10 operand: 17
6	Operation	operator: 10 operand: 18
7	Literal
8	ExprTuple	12, 13, 14, 15, 16
9	ExprTuple	17
10	Literal
11	ExprTuple	18
12	ExprTuple	21, 29
13	ExprTuple	30, 19
14	ExprTuple	20, 21
15	ExprTuple	27, 22
16	ExprTuple	22, 27
17	Variable
18	Variable
19	Operation	operator: 25 operands: 23
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	ExprTuple	29, 27
24	ExprTuple	30, 28
25	Literal
26	ExprTuple	29, 30
27	Literal
28	Variable
29	Variable
30	Variable