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, j, k, n
from proveit.logic import And, InSet, NotEquals
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = Lambda([j, k], Conditional(NotEquals(NumKet(j, n), NumKet(k, n)), And(InSet(j, n_bit_interval), InSet(k, n_bit_interval), NotEquals(j, k))))

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(j, k\right) \mapsto \left\{\lvert j \rangle_{n} \neq \lvert k \rangle_{n} \textrm{ if } j \in \{0~\ldotp \ldotp~2^{n} - 1\} ,  k \in \{0~\ldotp \ldotp~2^{n} - 1\} ,  j \neq k\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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