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 b, l
from proveit.logic import Forall, NotEquals, NotInSet, Set
from proveit.numbers import Integer, frac, subtract, zero
from proveit.physics.quantum.QPE import _b_floor, _b_round, _delta_b, _full_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [b, l], instance_expr = NotInSet(subtract(_delta_b, frac(l, _two_pow_t)), Integer), domains = [Set(_b_floor, _b_round), _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_{b \in \left\{b_{\textit{f}}, b_{\textit{r}}\right\}, l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}~|~l \neq 0}~\left(\left(\delta_{b} - \frac{l}{2^{t}}\right) \notin \mathbb{Z}\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	parameters: 4 body: 5
4	ExprTuple	35, 43
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, 16
12	Operation	operator: 53 operands: 17
13	Literal
14	Operation	operator: 19 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operands: 22
17	ExprTuple	23, 24
18	ExprTuple	35, 25
19	Literal
20	ExprTuple	43, 26
21	Literal
22	ExprTuple	43, 27
23	Operation	operator: 28 operand: 35
24	Operation	operator: 57 operand: 36
25	Operation	operator: 31 operands: 32
26	Operation	operator: 33 operands: 34
27	Literal
28	Literal
29	ExprTuple	35
30	ExprTuple	36
31	Literal
32	ExprTuple	37, 38
33	Literal
34	ExprTuple	39, 48
35	Variable
36	Operation	operator: 40 operands: 41
37	Literal
38	Literal
39	Operation	operator: 53 operands: 42
40	Literal
41	ExprTuple	43, 44
42	ExprTuple	45, 59
43	Variable
44	Operation	operator: 49 operands: 46
45	Operation	operator: 57 operand: 48
46	ExprTuple	51, 55
47	ExprTuple	48
48	Operation	operator: 49 operands: 50
49	Literal
50	ExprTuple	51, 52
51	Literal
52	Operation	operator: 53 operands: 54
53	Literal
54	ExprTuple	55, 56
55	Literal
56	Operation	operator: 57 operand: 59
57	Literal
58	ExprTuple	59
59	Literal