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, l, n
from proveit.core_expr_types import A_1_to_l, C_1_to_n
from proveit.linear_algebra import ScalarMult
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 = [A_1_to_l, B, C_1_to_n], instance_expr = 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), condition = InClass(Qmult(A_1_to_l, B, C_1_to_n), QmultCodomain)), And(InSet(alpha, Complex), 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_{A_{1}, A_{2}, \ldots, A_{l}, B, C_{1}, C_{2}, \ldots, C_{n}~|~\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^*}}~\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}\right) \textrm{ if } \alpha \in \mathbb{C} ,  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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9, 10
7	Lambda	parameters: 31 body: 11
8	Operation	operator: 14 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	Conditional	value: 16 condition: 17
12	ExprTuple	42, 18
13	ExprTuple	38, 19
14	Literal
15	ExprTuple	41, 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 30 operands: 28
25	Operation	operator: 30 operands: 29
26	Operation	operator: 30 operands: 31
27	Literal
28	ExprTuple	33, 32, 34
29	ExprTuple	33, 42, 43, 34
30	Literal
31	ExprTuple	33, 43, 34
32	Operation	operator: 35 operands: 36
33	ExprRange	lambda_map: 37 start_index: 40 end_index: 38
34	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
35	Literal
36	ExprTuple	42, 43
37	Lambda	parameter: 49 body: 44
38	Variable
39	Lambda	parameter: 49 body: 45
40	Literal
41	Variable
42	Variable
43	Variable
44	IndexedVar	variable: 46 index: 49
45	IndexedVar	variable: 47 index: 49
46	Variable
47	Variable
48	ExprTuple	49
49	Variable