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, 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 = ExprTuple(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())

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