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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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