Expression of type ExprTuple

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, ExprTuple, Lambda, k, n
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, NaturalPos, one
from proveit.physics.quantum import NumKet, ket0
from proveit.physics.quantum.algebra import n_bit_interval

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [k], instance_expr = Equals(NumKet(k, Add(n, one)), TensorProd(ket0, 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())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 47 body: 3
2	ExprTuple	47
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 17 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	47, 10
9	Lambda	parameter: 39 body: 12
10	Literal
11	ExprTuple	39
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	39, 21
19	Operation	operator: 34 operands: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprTuple	39, 27
23	Literal
24	ExprTuple	28, 29
25	Literal
26	ExprTuple	38, 30
27	Operation	operator: 36 operands: 31
28	Operation	operator: 32 operand: 38
29	Operation	operator: 34 operands: 35
30	Operation	operator: 36 operands: 37
31	ExprTuple	47, 48
32	Literal
33	ExprTuple	38
34	Literal
35	ExprTuple	39, 47
36	Literal
37	ExprTuple	40, 41
38	Literal
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