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 InSet
from proveit.numbers import Abs, Exp, LessEq, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_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)))), InSet(l, _pos_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())

\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 \{e + 1~\ldotp \ldotp~2^{t - 1}\}\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: 44 body: 3
2	ExprTuple	44
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	44, 12
10	Operation	operator: 54 operands: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18, 58
14	Literal
15	ExprTuple	46, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 22 operand: 27
19	Operation	operator: 50 operands: 24
20	Operation	operator: 41 operands: 25
21	Operation	operator: 54 operands: 26
22	Literal
23	ExprTuple	27
24	ExprTuple	28, 29
25	ExprTuple	30, 46
26	ExprTuple	58, 31
27	Operation	operator: 32 operand: 36
28	Literal
29	Operation	operator: 54 operands: 34
30	Variable
31	Operation	operator: 41 operands: 35
32	Literal
33	ExprTuple	36
34	ExprTuple	37, 58
35	ExprTuple	59, 38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operands: 42
38	Operation	operator: 47 operand: 46
39	Literal
40	ExprTuple	60, 44
41	Literal
42	ExprTuple	44, 45
43	ExprTuple	46
44	Variable
45	Operation	operator: 47 operand: 49
46	Literal
47	Literal
48	ExprTuple	49
49	Operation	operator: 50 operands: 51
50	Literal
51	ExprTuple	52, 53
52	Operation	operator: 54 operands: 55
53	Operation	operator: 56 operand: 60
54	Literal
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	60
58	Literal
59	Literal
60	Literal