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, k
from proveit.logic import InSet
from proveit.numbers import Exp, LessEq, Mult, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(LessEq(frac(one, Exp(subtract(k, Mult(_two_pow_t, _delta_b_floor)), two)), frac(one, Exp(subtract(k, one), two))), InSet(k, _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())

k \mapsto \left\{\frac{1}{\left(k - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \leq \frac{1}{\left(k - 1\right)^{2}} \textrm{ if } k \in \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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