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 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 = ExprTuple(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())

\left(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..\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: 39 body: 3
2	ExprTuple	39
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	39, 12
10	Operation	operator: 24 operands: 13
11	Operation	operator: 45 operands: 14
12	Operation	operator: 15 operands: 16
13	ExprTuple	41, 17
14	ExprTuple	18, 19
15	Literal
16	ExprTuple	20, 21
17	Operation	operator: 45 operands: 22
18	Operation	operator: 24 operands: 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 36 operands: 26
21	Operation	operator: 49 operands: 27
22	ExprTuple	28, 29
23	ExprTuple	41, 28
24	Literal
25	ExprTuple	41, 29
26	ExprTuple	30, 41
27	ExprTuple	53, 31
28	Literal
29	Operation	operator: 49 operands: 32
30	Variable
31	Operation	operator: 36 operands: 33
32	ExprTuple	34, 53
33	ExprTuple	54, 35
34	Operation	operator: 36 operands: 37
35	Operation	operator: 42 operand: 41
36	Literal
37	ExprTuple	39, 40
38	ExprTuple	41
39	Variable
40	Operation	operator: 42 operand: 44
41	Literal
42	Literal
43	ExprTuple	44
44	Operation	operator: 45 operands: 46
45	Literal
46	ExprTuple	47, 48
47	Operation	operator: 49 operands: 50
48	Operation	operator: 51 operand: 55
49	Literal
50	ExprTuple	53, 54
51	Literal
52	ExprTuple	55
53	Literal
54	Literal
55	Literal