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, Less, frac, one, subtract, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

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