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
from proveit.numbers import Abs, Exp, LessEq, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_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 = _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} \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	47, 14
12	Operation	operator: 62 operands: 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	20, 66
16	Literal
17	ExprTuple	61, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 24 operand: 29
21	Operation	operator: 55 operands: 26
22	Operation	operator: 51 operands: 27
23	Operation	operator: 57 operand: 33
24	Literal
25	ExprTuple	29
26	ExprTuple	30, 31
27	ExprTuple	32, 61
28	ExprTuple	33
29	Operation	operator: 34 operand: 39
30	Literal
31	Operation	operator: 62 operands: 36
32	Operation	operator: 57 operand: 41
33	Operation	operator: 51 operands: 38
34	Literal
35	ExprTuple	39
36	ExprTuple	40, 66
37	ExprTuple	41
38	ExprTuple	42, 61
39	Operation	operator: 43 operands: 44
40	Operation	operator: 51 operands: 45
41	Operation	operator: 62 operands: 46
42	Variable
43	Literal
44	ExprTuple	68, 47
45	ExprTuple	47, 48
46	ExprTuple	66, 49
47	Variable
48	Operation	operator: 57 operand: 53
49	Operation	operator: 51 operands: 52
50	ExprTuple	53
51	Literal
52	ExprTuple	67, 54
53	Operation	operator: 55 operands: 56
54	Operation	operator: 57 operand: 61
55	Literal
56	ExprTuple	59, 60
57	Literal
58	ExprTuple	61
59	Operation	operator: 62 operands: 63
60	Operation	operator: 64 operand: 68
61	Literal
62	Literal
63	ExprTuple	66, 67
64	Literal
65	ExprTuple	68
66	Literal
67	Literal
68	Literal