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 Equals, Forall
from proveit.numbers import Exp, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain

# build up the expression from sub-expressions
sub_expr1 = Exp(_diff_l_scaled_delta_floor, two)
expr = Forall(instance_param_or_params = [l], instance_expr = Equals(frac(one, Mult(four, sub_expr1)), Mult(frac(one, four), frac(one, sub_expr1))), 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}} = \left(\frac{1}{4} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{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: 42 body: 5
4	ExprTuple	42
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	42, 14
12	Operation	operator: 26 operands: 15
13	Operation	operator: 50 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	56, 19
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	22, 23
19	Operation	operator: 50 operands: 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 46 operands: 28
23	Operation	operator: 52 operand: 33
24	ExprTuple	30, 31
25	ExprTuple	56, 30
26	Literal
27	ExprTuple	56, 31
28	ExprTuple	32, 56
29	ExprTuple	33
30	Literal
31	Operation	operator: 57 operands: 34
32	Operation	operator: 52 operand: 38
33	Operation	operator: 46 operands: 36
34	ExprTuple	37, 61
35	ExprTuple	38
36	ExprTuple	39, 56
37	Operation	operator: 46 operands: 40
38	Operation	operator: 57 operands: 41
39	Variable
40	ExprTuple	42, 43
41	ExprTuple	61, 44
42	Variable
43	Operation	operator: 52 operand: 48
44	Operation	operator: 46 operands: 47
45	ExprTuple	48
46	Literal
47	ExprTuple	62, 49
48	Operation	operator: 50 operands: 51
49	Operation	operator: 52 operand: 56
50	Literal
51	ExprTuple	54, 55
52	Literal
53	ExprTuple	56
54	Operation	operator: 57 operands: 58
55	Operation	operator: 59 operand: 63
56	Literal
57	Literal
58	ExprTuple	61, 62
59	Literal
60	ExprTuple	63
61	Literal
62	Literal
63	Literal