Expression of type Lambda

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, Lambda, l
from proveit.logic import And, Equals, InSet, 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 = Lambda(l, Conditional(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)))))))), And(InSet(l, _full_domain), 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())

l \mapsto \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) \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} ,  l \neq 0\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 80 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 12 operand: 19
9	Operation	operator: 68 operands: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	19
14	ExprTuple	20, 21
15	Literal
16	ExprTuple	80, 22
17	Literal
18	ExprTuple	80, 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 77 operands: 26
21	Operation	operator: 77 operands: 27
22	Operation	operator: 28 operands: 29
23	Literal
24	Literal
25	ExprTuple	79, 80
26	ExprTuple	67, 81
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32, 44
30	Operation	operator: 61 operands: 33
31	Operation	operator: 61 operands: 34
32	Operation	operator: 61 operands: 35
33	ExprTuple	67, 36
34	ExprTuple	67, 37
35	ExprTuple	38, 67
36	Operation	operator: 71 operand: 42
37	Operation	operator: 71 operand: 43
38	Operation	operator: 71 operand: 44
39	ExprTuple	42
40	ExprTuple	43
41	ExprTuple	44
42	Operation	operator: 82 operands: 45
43	Operation	operator: 82 operands: 46
44	Operation	operator: 82 operands: 47
45	ExprTuple	49, 48
46	ExprTuple	49, 50
47	ExprTuple	84, 51
48	Operation	operator: 68 operands: 52
49	Literal
50	Operation	operator: 68 operands: 53
51	Operation	operator: 61 operands: 54
52	ExprTuple	84, 56, 57, 55
53	ExprTuple	84, 56, 57, 58
54	ExprTuple	85, 59
55	Operation	operator: 61 operands: 60
56	Literal
57	Literal
58	Operation	operator: 61 operands: 62
59	Operation	operator: 71 operand: 67
60	ExprTuple	64, 65
61	Literal
62	ExprTuple	73, 66
63	ExprTuple	67
64	Operation	operator: 68 operands: 69
65	Operation	operator: 71 operand: 80
66	Operation	operator: 71 operand: 74
67	Literal
68	Literal
69	ExprTuple	81, 73
70	ExprTuple	80
71	Literal
72	ExprTuple	74
73	Operation	operator: 75 operand: 79
74	Operation	operator: 77 operands: 78
75	Literal
76	ExprTuple	79
77	Literal
78	ExprTuple	80, 81
79	Literal
80	Variable
81	Operation	operator: 82 operands: 83
82	Literal
83	ExprTuple	84, 85
84	Literal
85	Literal