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
from proveit.numbers import IntervalCO, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _full_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = frac(one, two)
expr = Forall(instance_param_or_params = [l], instance_expr = InSet(subtract(_delta_b_floor, frac(l, _two_pow_t)), IntervalCO(Neg(sub_expr1), sub_expr1)), domain = _full_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~2^{t - 1}\}}~\left(\left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right) \in \left[-\frac{1}{2},\frac{1}{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: 36 body: 5
4	ExprTuple	36
5	Conditional	value: 6 condition: 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	36, 13
11	Operation	operator: 44 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21, 30
17	Literal
18	ExprTuple	22, 38
19	Operation	operator: 23 operand: 28
20	Operation	operator: 48 operand: 29
21	Operation	operator: 48 operand: 30
22	Operation	operator: 44 operands: 27
23	Literal
24	ExprTuple	28
25	ExprTuple	29
26	ExprTuple	30
27	ExprTuple	31, 50
28	Literal
29	Operation	operator: 33 operands: 32
30	Operation	operator: 33 operands: 34
31	Operation	operator: 48 operand: 38
32	ExprTuple	36, 37
33	Literal
34	ExprTuple	50, 42
35	ExprTuple	38
36	Variable
37	Operation	operator: 40 operands: 39
38	Operation	operator: 40 operands: 41
39	ExprTuple	42, 46
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Operation	operator: 48 operand: 50
48	Literal
49	ExprTuple	50
50	Literal