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
from proveit.core_expr_types import A_1_to_l, b_1_to_j
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Complex, Mult, Natural, NaturalPos
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], instance_expr = Equals(Qmult(b_1_to_j, A_1_to_l), Qmult(Mult(b_1_to_j), A_1_to_l)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l), QmultCodomain)), domain = Complex), And(InSet(j, NaturalPos), InSet(l, 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}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) =  \\ \left(\left(b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right)\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) \end{array} \end{array}\right)\right] \textrm{ if } j \in \mathbb{N}^+ ,  l \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: 15 operand: 5
2	Operation	operator: 17 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Lambda	parameters: 44 body: 8
6	Operation	operator: 30 operands: 9
7	Operation	operator: 30 operands: 10
8	Conditional	value: 11 condition: 12
9	ExprTuple	51, 13
10	ExprTuple	46, 14
11	Operation	operator: 15 operand: 19
12	Operation	operator: 17 operands: 18
13	Literal
14	Literal
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	20
19	Lambda	parameters: 40 body: 21
20	ExprRange	lambda_map: 22 start_index: 50 end_index: 51
21	Conditional	value: 23 condition: 24
22	Lambda	parameter: 56 body: 25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	ExprTuple	32, 33
28	Literal
29	ExprTuple	34, 35
30	Literal
31	ExprTuple	53, 36
32	Operation	operator: 39 operands: 37
33	Operation	operator: 39 operands: 38
34	Operation	operator: 39 operands: 40
35	Literal
36	Literal
37	ExprTuple	47, 42
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	42
41	Operation	operator: 43 operands: 44
42	ExprRange	lambda_map: 45 start_index: 50 end_index: 46
43	Literal
44	ExprTuple	47
45	Lambda	parameter: 56 body: 48
46	Variable
47	ExprRange	lambda_map: 49 start_index: 50 end_index: 51
48	IndexedVar	variable: 52 index: 56
49	Lambda	parameter: 56 body: 53
50	Literal
51	Variable
52	Variable
53	IndexedVar	variable: 54 index: 56
54	Variable
55	ExprTuple	56
56	Variable