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 Forall, InSet, NotEquals
from proveit.numbers import NaturalPos
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [j, k], instance_expr = NotEquals(NumKet(j, n), NumKet(k, n)), domain = n_bit_interval, condition = NotEquals(j, k)), 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())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 45 body: 2
1	ExprTuple	45
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 25 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	45, 9
8	Lambda	parameters: 28 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 27 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19, 20
16	Operation	operator: 22 operands: 21
17	Operation	operator: 22 operands: 23
18	Operation	operator: 25 operands: 24
19	Operation	operator: 25 operands: 26
20	Operation	operator: 27 operands: 28
21	ExprTuple	30, 45
22	Literal
23	ExprTuple	31, 45
24	ExprTuple	30, 29
25	Literal
26	ExprTuple	31, 29
27	Literal
28	ExprTuple	30, 31
29	Operation	operator: 32 operands: 33
30	Variable
31	Variable
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
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