Expression of type Conditional

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 Conditional, j, l, n
from proveit.core_expr_types import A_1_to_l, C_1_to_n, b_1_to_j
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Complex, Natural
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [b_1_to_j], instance_expr = Forall(instance_param_or_params = [A_1_to_l, C_1_to_n], instance_expr = Equals(Qmult(A_1_to_l, b_1_to_j, C_1_to_n), Qmult(b_1_to_j, A_1_to_l, C_1_to_n)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l, C_1_to_n), QmultCodomain)), domain = Complex), And(InSet(j, Natural), InSet(l, Natural), InSet(n, Natural)))

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\{\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] \textrm{ if } j \in \mathbb{N} ,  l \in \mathbb{N} ,  n \in \mathbb{N}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 17 operand: 5
2	Operation	operator: 19 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7, 8
5	Lambda	parameters: 9 body: 10
6	Operation	operator: 32 operands: 11
7	Operation	operator: 32 operands: 12
8	Operation	operator: 32 operands: 13
9	ExprTuple	43
10	Conditional	value: 14 condition: 15
11	ExprTuple	47, 16
12	ExprTuple	49, 16
13	ExprTuple	52, 16
14	Operation	operator: 17 operand: 21
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21
19	Literal
20	ExprTuple	22
21	Lambda	parameters: 42 body: 23
22	ExprRange	lambda_map: 24 start_index: 51 end_index: 47
23	Conditional	value: 25 condition: 26
24	Lambda	parameter: 60 body: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Literal
29	ExprTuple	34, 35
30	Literal
31	ExprTuple	36, 37
32	Literal
33	ExprTuple	53, 38
34	Operation	operator: 41 operands: 39
35	Operation	operator: 41 operands: 40
36	Operation	operator: 41 operands: 42
37	Literal
38	Literal
39	ExprTuple	44, 43, 45
40	ExprTuple	43, 44, 45
41	Literal
42	ExprTuple	44, 45
43	ExprRange	lambda_map: 46 start_index: 51 end_index: 47
44	ExprRange	lambda_map: 48 start_index: 51 end_index: 49
45	ExprRange	lambda_map: 50 start_index: 51 end_index: 52
46	Lambda	parameter: 60 body: 53
47	Variable
48	Lambda	parameter: 60 body: 54
49	Variable
50	Lambda	parameter: 60 body: 55
51	Literal
52	Variable
53	IndexedVar	variable: 56 index: 60
54	IndexedVar	variable: 57 index: 60
55	IndexedVar	variable: 58 index: 60
56	Variable
57	Variable
58	Variable
59	ExprTuple	60
60	Variable