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 LinMap
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex, Exp, NaturalPos, two
from proveit.physics.quantum import NumBra
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 = InSet(NumBra(k, n), LinMap(CartExp(Complex, Exp(two, n)), Complex)), 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({_{n}}\langle k \rvert \in \mathcal{L}\left(\mathbb{C}^{2^{n}}, \mathbb{C}\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: 44 body: 4
3	ExprTuple	44
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 17 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	44, 11
10	Lambda	parameter: 28 body: 13
11	Literal
12	ExprTuple	28
13	Conditional	value: 14 condition: 15
14	Operation	operator: 17 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	28, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	28, 44
24	Literal
25	ExprTuple	29, 36
26	Literal
27	ExprTuple	30, 31
28	Variable
29	Operation	operator: 32 operands: 33
30	Literal
31	Operation	operator: 34 operands: 35
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	37, 38
36	Literal
37	Operation	operator: 39 operands: 40
38	Operation	operator: 41 operand: 45
39	Literal
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	45
43	Literal
44	Variable
45	Literal