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 Exp, Mult, Real, four, 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 = InSet(frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two))), Real), 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}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \in \mathbb{R}\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: 14 operands: 15
12	Literal
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	50, 18
16	Literal
17	ExprTuple	19, 20
18	Operation	operator: 44 operands: 21
19	Operation	operator: 40 operands: 22
20	Operation	operator: 46 operand: 27
21	ExprTuple	24, 25
22	ExprTuple	26, 50
23	ExprTuple	27
24	Literal
25	Operation	operator: 51 operands: 28
26	Operation	operator: 46 operand: 32
27	Operation	operator: 40 operands: 30
28	ExprTuple	31, 55
29	ExprTuple	32
30	ExprTuple	33, 50
31	Operation	operator: 40 operands: 34
32	Operation	operator: 51 operands: 35
33	Variable
34	ExprTuple	36, 37
35	ExprTuple	55, 38
36	Variable
37	Operation	operator: 46 operand: 42
38	Operation	operator: 40 operands: 41
39	ExprTuple	42
40	Literal
41	ExprTuple	56, 43
42	Operation	operator: 44 operands: 45
43	Operation	operator: 46 operand: 50
44	Literal
45	ExprTuple	48, 49
46	Literal
47	ExprTuple	50
48	Operation	operator: 51 operands: 52
49	Operation	operator: 53 operand: 57
50	Literal
51	Literal
52	ExprTuple	55, 56
53	Literal
54	ExprTuple	57
55	Literal
56	Literal
57	Literal