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 LinMap
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex, Exp, NaturalPos, two
from proveit.physics.quantum import NumBra
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 = InSet(NumBra(k, n), LinMap(CartExp(Complex, Exp(two, n)), Complex)), 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({_{n}}\langle k \rvert \in \mathcal{L}\left(\mathbb{C}^{2^{n}}, \mathbb{C}\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: 13 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	40, 7
6	Lambda	parameter: 24 body: 9
7	Literal
8	ExprTuple	24
9	Conditional	value: 10 condition: 11
10	Operation	operator: 13 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	24, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	24, 40
20	Literal
21	ExprTuple	25, 32
22	Literal
23	ExprTuple	26, 27
24	Variable
25	Operation	operator: 28 operands: 29
26	Literal
27	Operation	operator: 30 operands: 31
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	33, 34
32	Literal
33	Operation	operator: 35 operands: 36
34	Operation	operator: 37 operand: 41
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41
39	Literal
40	Variable
41	Literal