Expression of type ExprTuple

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, ExprTuple, Lambda, l
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Abs, Exp, LessEq, Mult, four, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _full_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(l, Conditional(LessEq(Exp(Abs(_rel_indexed_alpha), two), frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two)))), 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())

\left(l \mapsto \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \leq \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} ,  l \neq 0\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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