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, NotEquals
from proveit.numbers import Abs, IntervalOC, Mult, frac, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _delta_b_floor, _full_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = InSet(Mult(pi, Abs(subtract(_delta_b_floor, frac(l, _two_pow_t)))), IntervalOC(zero, frac(pi, 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(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\right) \in \left(0,\frac{\pi}{2}\right]\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: 50 body: 5
4	ExprTuple	50
5	Conditional	value: 6 condition: 7
6	Operation	operator: 19 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	Operation	operator: 19 operands: 20
14	Operation	operator: 21 operands: 22
15	Literal
16	ExprTuple	33, 23
17	Literal
18	ExprTuple	26, 24
19	Literal
20	ExprTuple	50, 25
21	Literal
22	ExprTuple	50, 26
23	Operation	operator: 27 operand: 32
24	Operation	operator: 47 operands: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	Literal
28	ExprTuple	32
29	ExprTuple	33, 57
30	Literal
31	ExprTuple	34, 46
32	Operation	operator: 55 operands: 35
33	Literal
34	Operation	operator: 55 operands: 36
35	ExprTuple	37, 38
36	ExprTuple	39, 62
37	Operation	operator: 40 operand: 44
38	Operation	operator: 60 operand: 45
39	Operation	operator: 60 operand: 46
40	Literal
41	ExprTuple	44
42	ExprTuple	45
43	ExprTuple	46
44	Literal
45	Operation	operator: 47 operands: 48
46	Operation	operator: 53 operands: 49
47	Literal
48	ExprTuple	50, 51
49	ExprTuple	57, 52
50	Variable
51	Operation	operator: 53 operands: 54
52	Operation	operator: 55 operands: 56
53	Literal
54	ExprTuple	57, 58
55	Literal
56	ExprTuple	58, 59
57	Literal
58	Literal
59	Operation	operator: 60 operand: 62
60	Literal
61	ExprTuple	62
62	Literal