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, Forall, InSet
from proveit.numbers import Add, Exp, NaturalPos, 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(n, Conditional(Forall(instance_param_or_params = [k], instance_expr = Equals(NumKet(Add(Exp(two, n), k), Add(n, one)), TensorProd(ket1, 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())

n \mapsto \left\{\forall_{k \in \{0~\ldotp \ldotp~2^{n} - 1\}}~\left(\lvert 2^{n} + k \rangle_{n + 1} = \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{n}\right)\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: 47 body: 2
1	ExprTuple	47
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 16 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	47, 9
8	Lambda	parameter: 39 body: 11
9	Literal
10	ExprTuple	39
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	39, 20
18	Operation	operator: 35 operands: 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	30, 31
26	Operation	operator: 37 operands: 32
27	Operation	operator: 37 operands: 33
28	Operation	operator: 34 operand: 48
29	Operation	operator: 35 operands: 36
30	Literal
31	Operation	operator: 37 operands: 38
32	ExprTuple	40, 39
33	ExprTuple	47, 48
34	Literal
35	Literal
36	ExprTuple	39, 47
37	Literal
38	ExprTuple	40, 41
39	Variable
40	Operation	operator: 42 operands: 43
41	Operation	operator: 44 operand: 48
42	Literal
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	48
46	Literal
47	Variable
48	Literal