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 ExprRange, IndexedVar, Variable, a, k
from proveit.core_expr_types import a_1_to_k
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Forall
from proveit.numbers import BinarySequence, Bit, one
from proveit.physics.quantum import Ket, NumKet

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [a_1_to_k], instance_expr = Equals(NumKet(BinarySequence(a_1_to_k), k), TensorProd(ExprRange(sub_expr1, Ket(IndexedVar(a, sub_expr1)), one, k))), domain = Bit)

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_{a_{1}, a_{2}, \ldots, a_{k} \in \mathbb{N}^{\leq 1}}~\left(\lvert \texttt{\#}\texttt{b}(a_{1}, a_{2}, \ldots, a_{k}) \rangle_{k} = \left(\lvert a_{1} \rangle {\otimes}  \lvert a_{2} \rangle {\otimes}  \ldots {\otimes}  \lvert a_{k} \rangle\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 23 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprRange	lambda_map: 18 start_index: 31 end_index: 32
14	Literal
15	ExprTuple	19, 32
16	Literal
17	ExprTuple	20
18	Lambda	parameter: 38 body: 21
19	Operation	operator: 22 operands: 23
20	ExprRange	lambda_map: 24 start_index: 31 end_index: 32
21	Operation	operator: 25 operands: 26
22	Literal
23	ExprTuple	27
24	Lambda	parameter: 38 body: 28
25	Literal
26	ExprTuple	35, 29
27	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
28	Operation	operator: 33 operand: 35
29	Literal
30	Lambda	parameter: 38 body: 35
31	Literal
32	Variable
33	Literal
34	ExprTuple	35
35	IndexedVar	variable: 36 index: 38
36	Variable
37	ExprTuple	38
38	Variable