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, IntervalOC, Mult, frac, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _delta_b_floor, _full_domain, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(l, Conditional(InSet(Mult(pi, Abs(subtract(_delta_b_floor, frac(l, _two_pow_t)))), IntervalOC(zero, frac(pi, 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(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\right) \in \left(0,\frac{\pi}{2}\right] \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: 48 body: 3
2	ExprTuple	48
3	Conditional	value: 4 condition: 5
4	Operation	operator: 17 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 17 operands: 18
12	Operation	operator: 19 operands: 20
13	Literal
14	ExprTuple	31, 21
15	Literal
16	ExprTuple	24, 22
17	Literal
18	ExprTuple	48, 23
19	Literal
20	ExprTuple	48, 24
21	Operation	operator: 25 operand: 30
22	Operation	operator: 45 operands: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	Literal
26	ExprTuple	30
27	ExprTuple	31, 55
28	Literal
29	ExprTuple	32, 44
30	Operation	operator: 53 operands: 33
31	Literal
32	Operation	operator: 53 operands: 34
33	ExprTuple	35, 36
34	ExprTuple	37, 60
35	Operation	operator: 38 operand: 42
36	Operation	operator: 58 operand: 43
37	Operation	operator: 58 operand: 44
38	Literal
39	ExprTuple	42
40	ExprTuple	43
41	ExprTuple	44
42	Literal
43	Operation	operator: 45 operands: 46
44	Operation	operator: 51 operands: 47
45	Literal
46	ExprTuple	48, 49
47	ExprTuple	55, 50
48	Variable
49	Operation	operator: 51 operands: 52
50	Operation	operator: 53 operands: 54
51	Literal
52	ExprTuple	55, 56
53	Literal
54	ExprTuple	56, 57
55	Literal
56	Literal
57	Operation	operator: 58 operand: 60
58	Literal
59	ExprTuple	60
60	Literal