Theorem qmult_op_op_in_QmultCodomain of type Forall

from the theory of proveit.physics.quantum.algebra

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.algebra import qmult_op_op_in_QmultCodomain

# check that the built expression is the same as the stored expression
assert qmult_op_op_in_QmultCodomain.expr == stored_expr
assert qmult_op_op_in_QmultCodomain.expr._style_id == stored_expr._style_id
print("Passed sanity check: qmult_op_op_in_QmultCodomain matches stored_expr")

Passed sanity check: qmult_op_op_in_QmultCodomain matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{\mathcal{H}, X, Y \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\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)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	46, 47, 44
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 23 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12, 13
10	Lambda	parameters: 29 body: 14
11	Operation	operator: 21 operands: 15
12	Operation	operator: 21 operands: 16
13	Operation	operator: 21 operands: 17
14	Conditional	value: 18 condition: 19
15	ExprTuple	46, 20
16	ExprTuple	47, 20
17	ExprTuple	44, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Literal
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 39 operands: 29
26	Literal
27	Operation	operator: 31 operands: 30
28	Operation	operator: 31 operands: 32
29	ExprTuple	43, 45
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36
33	Operation	operator: 39 operand: 43
34	Operation	operator: 41 operands: 38
35	Operation	operator: 39 operand: 45
36	Operation	operator: 41 operands: 42
37	ExprTuple	43
38	ExprTuple	47, 44
39	Literal
40	ExprTuple	45
41	Literal
42	ExprTuple	46, 47
43	Variable
44	Variable
45	Variable
46	Variable
47	Variable