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, NotEquals
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _delta_b_floor, _full_domain, _rel_indexed_alpha, _two_pow_t

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l], instance_expr = Equals(_rel_indexed_alpha, Mult(frac(one, _two_pow_t), frac(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))), subtract(one, Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t)))))))), domain = _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_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}~|~l \neq 0}~\left(\alpha_{b_{\textit{f}} \oplus l} = \left(\frac{1}{2^{t}} \cdot \frac{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)}}\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: 83 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 15 operand: 22
12	Operation	operator: 71 operands: 17
13	Operation	operator: 18 operands: 19
14	Operation	operator: 20 operands: 21
15	Literal
16	ExprTuple	22
17	ExprTuple	23, 24
18	Literal
19	ExprTuple	83, 25
20	Literal
21	ExprTuple	83, 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 80 operands: 29
24	Operation	operator: 80 operands: 30
25	Operation	operator: 31 operands: 32
26	Literal
27	Literal
28	ExprTuple	82, 83
29	ExprTuple	70, 84
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 47
33	Operation	operator: 64 operands: 36
34	Operation	operator: 64 operands: 37
35	Operation	operator: 64 operands: 38
36	ExprTuple	70, 39
37	ExprTuple	70, 40
38	ExprTuple	41, 70
39	Operation	operator: 74 operand: 45
40	Operation	operator: 74 operand: 46
41	Operation	operator: 74 operand: 47
42	ExprTuple	45
43	ExprTuple	46
44	ExprTuple	47
45	Operation	operator: 85 operands: 48
46	Operation	operator: 85 operands: 49
47	Operation	operator: 85 operands: 50
48	ExprTuple	52, 51
49	ExprTuple	52, 53
50	ExprTuple	87, 54
51	Operation	operator: 71 operands: 55
52	Literal
53	Operation	operator: 71 operands: 56
54	Operation	operator: 64 operands: 57
55	ExprTuple	87, 59, 60, 58
56	ExprTuple	87, 59, 60, 61
57	ExprTuple	88, 62
58	Operation	operator: 64 operands: 63
59	Literal
60	Literal
61	Operation	operator: 64 operands: 65
62	Operation	operator: 74 operand: 70
63	ExprTuple	67, 68
64	Literal
65	ExprTuple	76, 69
66	ExprTuple	70
67	Operation	operator: 71 operands: 72
68	Operation	operator: 74 operand: 83
69	Operation	operator: 74 operand: 77
70	Literal
71	Literal
72	ExprTuple	84, 76
73	ExprTuple	83
74	Literal
75	ExprTuple	77
76	Operation	operator: 78 operand: 82
77	Operation	operator: 80 operands: 81
78	Literal
79	ExprTuple	82
80	Literal
81	ExprTuple	83, 84
82	Literal
83	Variable
84	Operation	operator: 85 operands: 86
85	Literal
86	ExprTuple	87, 88
87	Literal
88	Literal