Expression of type Forall

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 k, n
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Forall
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 = Forall(instance_param_or_params = [n], instance_expr = 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), domain = 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())

\forall_{n \in \mathbb{N}^+}~\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)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 49 body: 4
3	ExprTuple	49
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 18 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	49, 11
10	Lambda	parameter: 41 body: 13
11	Literal
12	ExprTuple	41
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	41, 22
20	Operation	operator: 37 operands: 23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	32, 33
28	Operation	operator: 39 operands: 34
29	Operation	operator: 39 operands: 35
30	Operation	operator: 36 operand: 50
31	Operation	operator: 37 operands: 38
32	Literal
33	Operation	operator: 39 operands: 40
34	ExprTuple	42, 41
35	ExprTuple	49, 50
36	Literal
37	Literal
38	ExprTuple	41, 49
39	Literal
40	ExprTuple	42, 43
41	Variable
42	Operation	operator: 44 operands: 45
43	Operation	operator: 46 operand: 50
44	Literal
45	ExprTuple	48, 49
46	Literal
47	ExprTuple	50
48	Literal
49	Variable
50	Literal