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, NaturalPos, one
from proveit.physics.quantum import NumKet, ket0
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(k, Add(n, one)), TensorProd(ket0, 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 k \rangle_{n + 1} = \left(\lvert 0 \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	44, 7
6	Lambda	parameter: 36 body: 9
7	Literal
8	ExprTuple	36
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	36, 18
16	Operation	operator: 31 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	36, 24
20	Literal
21	ExprTuple	25, 26
22	Literal
23	ExprTuple	35, 27
24	Operation	operator: 33 operands: 28
25	Operation	operator: 29 operand: 35
26	Operation	operator: 31 operands: 32
27	Operation	operator: 33 operands: 34
28	ExprTuple	44, 45
29	Literal
30	ExprTuple	35
31	Literal
32	ExprTuple	36, 44
33	Literal
34	ExprTuple	37, 38
35	Literal
36	Variable
37	Operation	operator: 39 operands: 40
38	Operation	operator: 41 operand: 45
39	Literal
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	45
43	Literal
44	Variable
45	Literal