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, b, l, n
from proveit.core_expr_types import A_1_to_l, C_1_to_n
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], instance_expr = Forall(instance_param_or_params = [A_1_to_l, C_1_to_n], instance_expr = Equals(Qmult(A_1_to_l, b, C_1_to_n), Qmult(b, 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(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 \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\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(b\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 } 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: 16 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	7, 8
6	Lambda	parameter: 37 body: 10
7	Operation	operator: 18 operands: 11
8	Operation	operator: 18 operands: 12
9	ExprTuple	37
10	Conditional	value: 13 condition: 14
11	ExprTuple	41, 15
12	ExprTuple	44, 15
13	Operation	operator: 16 operand: 20
14	Operation	operator: 18 operands: 19
15	Literal
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	37, 21
20	Lambda	parameters: 36 body: 22
21	Literal
22	Conditional	value: 23 condition: 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 32
29	Operation	operator: 35 operands: 33
30	Operation	operator: 35 operands: 34
31	Operation	operator: 35 operands: 36
32	Literal
33	ExprTuple	38, 37, 39
34	ExprTuple	37, 38, 39
35	Literal
36	ExprTuple	38, 39
37	Variable
38	ExprRange	lambda_map: 40 start_index: 43 end_index: 41
39	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
40	Lambda	parameter: 50 body: 45
41	Variable
42	Lambda	parameter: 50 body: 46
43	Literal
44	Variable
45	IndexedVar	variable: 47 index: 50
46	IndexedVar	variable: 48 index: 50
47	Variable
48	Variable
49	ExprTuple	50
50	Variable