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 Equals, InSet
from proveit.numbers import Exp, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = Exp(_diff_l_scaled_delta_floor, two)
expr = Lambda(l, Conditional(Equals(frac(one, Mult(four, sub_expr1)), Mult(frac(one, four), frac(one, sub_expr1))), 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())

l \mapsto \left\{\frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} = \left(\frac{1}{4} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) \textrm{ if } l \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: 38 body: 2
1	ExprTuple	38
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	38, 11
9	Operation	operator: 23 operands: 12
10	Operation	operator: 44 operands: 13
11	Operation	operator: 14 operands: 15
12	ExprTuple	40, 16
13	ExprTuple	17, 18
14	Literal
15	ExprTuple	19, 20
16	Operation	operator: 44 operands: 21
17	Operation	operator: 23 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 35 operands: 25
20	Operation	operator: 48 operands: 26
21	ExprTuple	27, 28
22	ExprTuple	40, 27
23	Literal
24	ExprTuple	40, 28
25	ExprTuple	29, 40
26	ExprTuple	52, 30
27	Literal
28	Operation	operator: 48 operands: 31
29	Variable
30	Operation	operator: 35 operands: 32
31	ExprTuple	33, 52
32	ExprTuple	53, 34
33	Operation	operator: 35 operands: 36
34	Operation	operator: 41 operand: 40
35	Literal
36	ExprTuple	38, 39
37	ExprTuple	40
38	Variable
39	Operation	operator: 41 operand: 43
40	Literal
41	Literal
42	ExprTuple	43
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Operation	operator: 48 operands: 49
47	Operation	operator: 50 operand: 54
48	Literal
49	ExprTuple	52, 53
50	Literal
51	ExprTuple	54
52	Literal
53	Literal
54	Literal