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 j, k, n
from proveit.logic import Forall, 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 = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [j, k], instance_expr = NotEquals(NumKet(j, n), NumKet(k, n)), domain = n_bit_interval, condition = NotEquals(j, k)), 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_{j, k \in \{0~\ldotp \ldotp~2^{n} - 1\}~|~j \neq k}~\left(\lvert j \rangle_{n} \neq \lvert k \rangle_{n}\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: 47 body: 4
3	ExprTuple	47
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 27 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	47, 11
10	Lambda	parameters: 30 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 29 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	Operation	operator: 24 operands: 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 27 operands: 26
21	Operation	operator: 27 operands: 28
22	Operation	operator: 29 operands: 30
23	ExprTuple	32, 47
24	Literal
25	ExprTuple	33, 47
26	ExprTuple	32, 31
27	Literal
28	ExprTuple	33, 31
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 34 operands: 35
32	Variable
33	Variable
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Operation	operator: 38 operands: 39
38	Literal
39	ExprTuple	40, 41
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