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 Exp, LessEq, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = LessEq(frac(one, Exp(_diff_l_scaled_delta_floor, two)), frac(one, Exp(l, 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(\frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \leq \frac{1}{l^{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: 34 body: 5
4	ExprTuple	34
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	34, 14
12	Operation	operator: 16 operands: 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	58, 20
16	Literal
17	ExprTuple	58, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 49 operands: 24
21	Operation	operator: 49 operands: 25
22	Operation	operator: 44 operands: 26
23	Operation	operator: 53 operand: 30
24	ExprTuple	28, 55
25	ExprTuple	34, 55
26	ExprTuple	29, 58
27	ExprTuple	30
28	Operation	operator: 44 operands: 31
29	Operation	operator: 53 operand: 36
30	Operation	operator: 44 operands: 33
31	ExprTuple	34, 35
32	ExprTuple	36
33	ExprTuple	37, 58
34	Variable
35	Operation	operator: 53 operand: 40
36	Operation	operator: 49 operands: 39
37	Variable
38	ExprTuple	40
39	ExprTuple	55, 41
40	Operation	operator: 42 operands: 43
41	Operation	operator: 44 operands: 45
42	Literal
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	56, 48
46	Operation	operator: 49 operands: 50
47	Operation	operator: 51 operand: 57
48	Operation	operator: 53 operand: 58
49	Literal
50	ExprTuple	55, 56
51	Literal
52	ExprTuple	57
53	Literal
54	ExprTuple	58
55	Literal
56	Literal
57	Literal
58	Literal