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, ExprRange, IndexedVar, Variable, b, j
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, one
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(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)), And(ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j)))

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_{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) \textrm{ if } \left(b_{1} \in \mathbb{C}\right) \land  \left(b_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(b_{j} \in \mathbb{C}\right)\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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	Lambda	parameters: 28 body: 9
8	ExprRange	lambda_map: 10 start_index: 37 end_index: 33
9	Conditional	value: 11 condition: 12
10	Lambda	parameter: 46 body: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	20, 21
16	Literal
17	ExprTuple	22, 23
18	Literal
19	ExprTuple	39, 24
20	Operation	operator: 27 operands: 25
21	Operation	operator: 27 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	Literal
25	ExprTuple	30, 29, 31
26	ExprTuple	29, 30, 31
27	Literal
28	ExprTuple	30, 31
29	ExprRange	lambda_map: 32 start_index: 37 end_index: 33
30	ExprRange	lambda_map: 34 start_index: 37 end_index: 35
31	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
32	Lambda	parameter: 46 body: 39
33	Variable
34	Lambda	parameter: 46 body: 40
35	Variable
36	Lambda	parameter: 46 body: 41
37	Literal
38	Variable
39	IndexedVar	variable: 42 index: 46
40	IndexedVar	variable: 43 index: 46
41	IndexedVar	variable: 44 index: 46
42	Variable
43	Variable
44	Variable
45	ExprTuple	46
46	Variable