Expression of type Equals

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, _neg_domain

# build up the expression from sub-expressions
sub_expr1 = Exp(_diff_l_scaled_delta_floor, two)
sub_expr2 = InSet(l, _neg_domain)
expr = Equals(Lambda(l, Conditional(frac(one, Mult(four, sub_expr1)), sub_expr2)), Lambda(l, Conditional(Mult(frac(one, four), frac(one, sub_expr1)), sub_expr2))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left[l \mapsto \left\{\frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right..\right] =  \\ \left[l \mapsto \left\{\frac{1}{4} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right..\right] \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Lambda	parameter: 38 body: 5
4	Lambda	parameter: 38 body: 7
5	Conditional	value: 8 condition: 10
6	ExprTuple	38
7	Conditional	value: 9 condition: 10
8	Operation	operator: 21 operands: 11
9	Operation	operator: 46 operands: 12
10	Operation	operator: 13 operands: 14
11	ExprTuple	62, 15
12	ExprTuple	16, 17
13	Literal
14	ExprTuple	38, 18
15	Operation	operator: 46 operands: 19
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	ExprTuple	25, 26
20	ExprTuple	62, 25
21	Literal
22	ExprTuple	62, 26
23	Literal
24	ExprTuple	27, 28
25	Literal
26	Operation	operator: 53 operands: 29
27	Operation	operator: 48 operands: 30
28	Operation	operator: 57 operand: 34
29	ExprTuple	32, 59
30	ExprTuple	33, 62
31	ExprTuple	34
32	Operation	operator: 48 operands: 35
33	Operation	operator: 57 operand: 40
34	Operation	operator: 48 operands: 37
35	ExprTuple	38, 39
36	ExprTuple	40
37	ExprTuple	41, 62
38	Variable
39	Operation	operator: 57 operand: 44
40	Operation	operator: 53 operands: 43
41	Variable
42	ExprTuple	44
43	ExprTuple	59, 45
44	Operation	operator: 46 operands: 47
45	Operation	operator: 48 operands: 49
46	Literal
47	ExprTuple	50, 51
48	Literal
49	ExprTuple	60, 52
50	Operation	operator: 53 operands: 54
51	Operation	operator: 55 operand: 61
52	Operation	operator: 57 operand: 62
53	Literal
54	ExprTuple	59, 60
55	Literal
56	ExprTuple	61
57	Literal
58	ExprTuple	62
59	Literal
60	Literal
61	Literal
62	Literal