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, a, k
from proveit.core_expr_types import a_1_to_k
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import BinarySequence, Bit, NaturalPos, one
from proveit.physics.quantum import Ket, NumKet

# 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_k], instance_expr = Equals(NumKet(BinarySequence(a_1_to_k), k), TensorProd(ExprRange(sub_expr1, Ket(IndexedVar(a, sub_expr1)), one, k))), domain = Bit), InSet(k, NaturalPos))

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_{k} \in \mathbb{N}^{\leq 1}}~\left(\lvert \texttt{\#}\texttt{b}(a_{1}, a_{2}, \ldots, a_{k}) \rangle_{k} = \left(\lvert a_{1} \rangle {\otimes}  \lvert a_{2} \rangle {\otimes}  \ldots {\otimes}  \lvert a_{k} \rangle\right)\right) \textrm{ if } k \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: 6
2	Operation	operator: 29 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	36, 7
6	Lambda	parameters: 27 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	ExprRange	lambda_map: 22 start_index: 35 end_index: 36
18	Literal
19	ExprTuple	23, 36
20	Literal
21	ExprTuple	24
22	Lambda	parameter: 42 body: 25
23	Operation	operator: 26 operands: 27
24	ExprRange	lambda_map: 28 start_index: 35 end_index: 36
25	Operation	operator: 29 operands: 30
26	Literal
27	ExprTuple	31
28	Lambda	parameter: 42 body: 32
29	Literal
30	ExprTuple	39, 33
31	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
32	Operation	operator: 37 operand: 39
33	Literal
34	Lambda	parameter: 42 body: 39
35	Literal
36	Variable
37	Literal
38	ExprTuple	39
39	IndexedVar	variable: 40 index: 42
40	Variable
41	ExprTuple	42
42	Variable