Theorem qmult_pulling_scalars_out_front 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_pulling_scalars_out_front

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

Passed sanity check: qmult_pulling_scalars_out_front matches stored_expr

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

\forall_{j, l, n \in \mathbb{N}}~\left[\forall_{b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}, C_{1}, C_{2}, \ldots, C_{n}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \end{array} \end{array}\right)\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: 21 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	51, 53, 56
4	Conditional	value: 5 condition: 6
5	Operation	operator: 21 operand: 9
6	Operation	operator: 23 operands: 8
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 13 body: 14
10	Operation	operator: 36 operands: 15
11	Operation	operator: 36 operands: 16
12	Operation	operator: 36 operands: 17
13	ExprTuple	47
14	Conditional	value: 18 condition: 19
15	ExprTuple	51, 20
16	ExprTuple	53, 20
17	ExprTuple	56, 20
18	Operation	operator: 21 operand: 25
19	Operation	operator: 23 operands: 24
20	Literal
21	Literal
22	ExprTuple	25
23	Literal
24	ExprTuple	26
25	Lambda	parameters: 46 body: 27
26	ExprRange	lambda_map: 28 start_index: 55 end_index: 51
27	Conditional	value: 29 condition: 30
28	Lambda	parameter: 64 body: 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 36 operands: 37
32	Literal
33	ExprTuple	38, 39
34	Literal
35	ExprTuple	40, 41
36	Literal
37	ExprTuple	57, 42
38	Operation	operator: 45 operands: 43
39	Operation	operator: 45 operands: 44
40	Operation	operator: 45 operands: 46
41	Literal
42	Literal
43	ExprTuple	48, 47, 49
44	ExprTuple	47, 48, 49
45	Literal
46	ExprTuple	48, 49
47	ExprRange	lambda_map: 50 start_index: 55 end_index: 51
48	ExprRange	lambda_map: 52 start_index: 55 end_index: 53
49	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
50	Lambda	parameter: 64 body: 57
51	Variable
52	Lambda	parameter: 64 body: 58
53	Variable
54	Lambda	parameter: 64 body: 59
55	Literal
56	Variable
57	IndexedVar	variable: 60 index: 64
58	IndexedVar	variable: 61 index: 64
59	IndexedVar	variable: 62 index: 64
60	Variable
61	Variable
62	Variable
63	ExprTuple	64
64	Variable