Expression of type Lambda

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, Lambda, k, n
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Exp, 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 = Lambda(k, Conditional(Equals(NumKet(Add(Exp(two, n), k), Add(n, one)), TensorProd(ket1, NumKet(k, n))), InSet(k, n_bit_interval)))

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())

k \mapsto \left\{\lvert 2^{n} + k \rangle_{n + 1} = \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{n}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{n} - 1\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 30 body: 2
1	ExprTuple	30
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	30, 11
9	Operation	operator: 26 operands: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21, 22
17	Operation	operator: 28 operands: 23
18	Operation	operator: 28 operands: 24
19	Operation	operator: 25 operand: 39
20	Operation	operator: 26 operands: 27
21	Literal
22	Operation	operator: 28 operands: 29
23	ExprTuple	31, 30
24	ExprTuple	38, 39
25	Literal
26	Literal
27	ExprTuple	30, 38
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operand: 39
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	39
37	Literal
38	Variable
39	Literal