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 B, Conditional, alpha
from proveit.core_expr_types import A_1_to_l, C_1_to_n
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals, InClass
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Conditional(Equals(Qmult(A_1_to_l, ScalarMult(alpha, B), C_1_to_n), Qmult(A_1_to_l, alpha, B, C_1_to_n)).with_wrapping_at(2), InClass(Qmult(A_1_to_l, B, C_1_to_n), QmultCodomain))

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\{\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace \left(\alpha \cdot B\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace \alpha \thinspace B\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \end{array} \end{array} \textrm{ if } \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) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 13 operands: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Literal
11	ExprTuple	16, 15, 17
12	ExprTuple	16, 25, 26, 17
13	Literal
14	ExprTuple	16, 26, 17
15	Operation	operator: 18 operands: 19
16	ExprRange	lambda_map: 20 start_index: 23 end_index: 21
17	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
18	Literal
19	ExprTuple	25, 26
20	Lambda	parameter: 32 body: 27
21	Variable
22	Lambda	parameter: 32 body: 28
23	Literal
24	Variable
25	Variable
26	Variable
27	IndexedVar	variable: 29 index: 32
28	IndexedVar	variable: 30 index: 32
29	Variable
30	Variable
31	ExprTuple	32
32	Variable