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, k, n
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Exp, NaturalPos, one, two
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [k], instance_expr = Equals(NumKet(Add(Exp(two, n), k), Add(n, one)), TensorProd(ket1, NumKet(k, n))), domain = n_bit_interval), InSet(n, 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_{k \in \{0~\ldotp \ldotp~2^{n} - 1\}}~\left(\lvert 2^{n} + k \rangle_{n + 1} = \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{n}\right)\right) \textrm{ if } 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: 6
2	Operation	operator: 14 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	45, 7
6	Lambda	parameter: 37 body: 9
7	Literal
8	ExprTuple	37
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	37, 18
16	Operation	operator: 33 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28, 29
24	Operation	operator: 35 operands: 30
25	Operation	operator: 35 operands: 31
26	Operation	operator: 32 operand: 46
27	Operation	operator: 33 operands: 34
28	Literal
29	Operation	operator: 35 operands: 36
30	ExprTuple	38, 37
31	ExprTuple	45, 46
32	Literal
33	Literal
34	ExprTuple	37, 45
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Operation	operator: 40 operands: 41
39	Operation	operator: 42 operand: 46
40	Literal
41	ExprTuple	44, 45
42	Literal
43	ExprTuple	46
44	Literal
45	Variable
46	Literal