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 ExprTuple, k, l
from proveit.logic import Forall
from proveit.numbers import Exp, LessEq, Mult, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _diff_l_scaled_delta_floor, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = [l]
expr = ExprTuple(Forall(instance_param_or_params = [k], instance_expr = LessEq(frac(one, Exp(subtract(k, Mult(_two_pow_t, _delta_b_floor)), two)), frac(one, Exp(subtract(k, one), two))), domain = _pos_domain), LessEq(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), domain = _pos_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(subtract(l, one), two)), domain = _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(\forall_{k \in \{e + 1~\ldotp \ldotp~2^{t - 1}\}}~\left(\frac{1}{\left(k - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \leq \frac{1}{\left(k - 1\right)^{2}}\right), \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) \leq \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - 1\right)^{2}}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 18 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 59 body: 10
7	Operation	operator: 12 operand: 16
8	Operation	operator: 12 operand: 17
9	ExprTuple	59
10	Conditional	value: 14 condition: 15
11	ExprTuple	16
12	Literal
13	ExprTuple	17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 34 operands: 20
16	Lambda	parameter: 61 body: 21
17	Lambda	parameter: 61 body: 23
18	Literal
19	ExprTuple	24, 25
20	ExprTuple	59, 40
21	Conditional	value: 26 condition: 28
22	ExprTuple	61
23	Conditional	value: 27 condition: 28
24	Operation	operator: 32 operands: 29
25	Operation	operator: 32 operands: 30
26	Operation	operator: 32 operands: 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 34 operands: 35
29	ExprTuple	75, 36
30	ExprTuple	75, 37
31	ExprTuple	75, 38
32	Literal
33	ExprTuple	75, 39
34	Literal
35	ExprTuple	61, 40
36	Operation	operator: 76 operands: 41
37	Operation	operator: 76 operands: 42
38	Operation	operator: 76 operands: 43
39	Operation	operator: 76 operands: 44
40	Operation	operator: 45 operands: 46
41	ExprTuple	47, 80
42	ExprTuple	48, 80
43	ExprTuple	49, 80
44	ExprTuple	50, 80
45	Literal
46	ExprTuple	51, 52
47	Operation	operator: 65 operands: 53
48	Operation	operator: 65 operands: 54
49	Operation	operator: 65 operands: 55
50	Operation	operator: 65 operands: 56
51	Operation	operator: 65 operands: 57
52	Operation	operator: 76 operands: 58
53	ExprTuple	59, 60
54	ExprTuple	59, 68
55	ExprTuple	61, 60
56	ExprTuple	61, 68
57	ExprTuple	62, 75
58	ExprTuple	80, 63
59	Variable
60	Operation	operator: 71 operand: 67
61	Variable
62	Variable
63	Operation	operator: 65 operands: 66
64	ExprTuple	67
65	Literal
66	ExprTuple	81, 68
67	Operation	operator: 69 operands: 70
68	Operation	operator: 71 operand: 75
69	Literal
70	ExprTuple	73, 74
71	Literal
72	ExprTuple	75
73	Operation	operator: 76 operands: 77
74	Operation	operator: 78 operand: 82
75	Literal
76	Literal
77	ExprTuple	80, 81
78	Literal
79	ExprTuple	82
80	Literal
81	Literal
82	Literal