Expression of type Forall

from the theory of proveit.physics.quantum.QPE

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 l
from proveit.logic import Forall, InSet
from proveit.numbers import Abs, Exp, Real, two
from proveit.physics.quantum.QPE import _neg_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = InSet(Exp(Abs(_rel_indexed_alpha), two), Real), domain = _neg_domain)

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_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}}~\left(\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \in \mathbb{R}\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	parameter: 39 body: 5
4	ExprTuple	39
5	Conditional	value: 6 condition: 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	39, 13
11	Operation	operator: 36 operands: 14
12	Literal
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 40
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 20 operand: 24
18	Operation	operator: 42 operands: 22
19	Operation	operator: 46 operand: 26
20	Literal
21	ExprTuple	24
22	ExprTuple	25, 48
23	ExprTuple	26
24	Operation	operator: 27 operand: 31
25	Operation	operator: 46 operand: 32
26	Operation	operator: 42 operands: 30
27	Literal
28	ExprTuple	31
29	ExprTuple	32
30	ExprTuple	33, 48
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Variable
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40, 41
38	Literal
39	Variable
40	Literal
41	Operation	operator: 42 operands: 43
42	Literal
43	ExprTuple	44, 45
44	Literal
45	Operation	operator: 46 operand: 48
46	Literal
47	ExprTuple	48
48	Literal