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, NotEquals
from proveit.numbers import Abs, Exp, LessEq, Mult, four, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _full_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = LessEq(Exp(Abs(_rel_indexed_alpha), two), frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two)))), domain = _full_domain, condition = NotEquals(l, zero))

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~2^{t - 1}\}~|~l \neq 0}~\left(\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \leq \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\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: 47 body: 5
4	ExprTuple	47
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 61 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operands: 20
15	Operation	operator: 21 operands: 22
16	ExprTuple	23, 67
17	Literal
18	ExprTuple	70, 24
19	Literal
20	ExprTuple	47, 25
21	Literal
22	ExprTuple	47, 26
23	Operation	operator: 27 operand: 32
24	Operation	operator: 54 operands: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	Literal
28	ExprTuple	32
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	35, 49
32	Operation	operator: 36 operand: 40
33	Literal
34	Operation	operator: 61 operands: 38
35	Operation	operator: 56 operands: 39
36	Literal
37	ExprTuple	40
38	ExprTuple	41, 67
39	ExprTuple	42, 70
40	Operation	operator: 43 operands: 44
41	Operation	operator: 56 operands: 45
42	Operation	operator: 65 operand: 49
43	Literal
44	ExprTuple	69, 47
45	ExprTuple	47, 48
46	ExprTuple	49
47	Variable
48	Operation	operator: 65 operand: 52
49	Operation	operator: 61 operands: 51
50	ExprTuple	52
51	ExprTuple	67, 53
52	Operation	operator: 54 operands: 55
53	Operation	operator: 56 operands: 57
54	Literal
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	68, 60
58	Operation	operator: 61 operands: 62
59	Operation	operator: 63 operand: 69
60	Operation	operator: 65 operand: 70
61	Literal
62	ExprTuple	67, 68
63	Literal
64	ExprTuple	69
65	Literal
66	ExprTuple	70
67	Literal
68	Literal
69	Literal
70	Literal