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 Conditional, e, l
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Abs, Add, Exp, Interval, Neg, one, subtract, two
from proveit.physics.quantum.QPE import _neg_domain, _rel_indexed_alpha, _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = Exp(Abs(_rel_indexed_alpha), two)
expr = Forall(instance_param_or_params = [l], instance_expr = Equals(Conditional(sub_expr1, InSet(l, _neg_domain)), Conditional(sub_expr1, InSet(l, Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), one))))).with_wrapping_at(1))

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}~\left(\begin{array}{c} \begin{array}{l} \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right.. \\  = \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-e - 1\}\right.. \end{array} \end{array}\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: 44 body: 5
4	ExprTuple	44
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Conditional	value: 11 condition: 10
9	Conditional	value: 11 condition: 12
10	Operation	operator: 15 operands: 13
11	Operation	operator: 47 operands: 14
12	Operation	operator: 15 operands: 16
13	ExprTuple	44, 17
14	ExprTuple	18, 49
15	Literal
16	ExprTuple	44, 19
17	Operation	operator: 23 operands: 20
18	Operation	operator: 21 operand: 26
19	Operation	operator: 23 operands: 24
20	ExprTuple	27, 25
21	Literal
22	ExprTuple	26
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 55 operand: 34
26	Operation	operator: 30 operand: 35
27	Operation	operator: 51 operands: 32
28	Operation	operator: 51 operands: 33
29	ExprTuple	34
30	Literal
31	ExprTuple	35
32	ExprTuple	36, 57
33	ExprTuple	37, 54
34	Operation	operator: 51 operands: 38
35	Operation	operator: 39 operands: 40
36	Operation	operator: 55 operand: 45
37	Operation	operator: 55 operand: 46
38	ExprTuple	46, 57
39	Literal
40	ExprTuple	43, 44
41	ExprTuple	45
42	ExprTuple	46
43	Literal
44	Variable
45	Operation	operator: 47 operands: 48
46	Variable
47	Literal
48	ExprTuple	49, 50
49	Literal
50	Operation	operator: 51 operands: 52
51	Literal
52	ExprTuple	53, 54
53	Literal
54	Operation	operator: 55 operand: 57
55	Literal
56	ExprTuple	57
57	Literal