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, Lambda, e, l
from proveit.logic import And, Forall, Iff, InSet, Union
from proveit.numbers import ModAbs, greater
from proveit.physics.quantum.QPE import _e_domain, _full_domain, _neg_domain, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = greater(ModAbs(l, _two_pow_t), e)
expr = ExprTuple(Lambda(l, Forall(instance_param_or_params = [e], instance_expr = Iff(And(InSet(l, Union(_neg_domain, _pos_domain)), sub_expr1), And(InSet(l, _full_domain), sub_expr1)).with_wrapping_at(1), domain = _e_domain).with_wrapping()))

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[\begin{array}{l}\forall_{e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(\left(l \in \left(\{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} \cup \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right)\right) \land \left(\left|l\right|_{\textup{mod}\thinspace 2^{t}} > e\right)\right) \\  \Leftrightarrow \left(\left(l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}\right) \land \left(\left|l\right|_{\textup{mod}\thinspace 2^{t}} > e\right)\right) \end{array} \end{array}\right)\end{array}\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: 43 body: 3
2	ExprTuple	43
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 58 body: 8
7	ExprTuple	58
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 26 operands: 13
11	Literal
12	ExprTuple	14, 15
13	ExprTuple	58, 16
14	Operation	operator: 18 operands: 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 46 operands: 20
17	ExprTuple	21, 23
18	Literal
19	ExprTuple	22, 23
20	ExprTuple	69, 24
21	Operation	operator: 26 operands: 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 63 operands: 30
25	ExprTuple	43, 31
26	Literal
27	ExprTuple	43, 32
28	Literal
29	ExprTuple	58, 33
30	ExprTuple	57, 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 46 operands: 37
33	Operation	operator: 38 operands: 39
34	Operation	operator: 67 operand: 61
35	Literal
36	ExprTuple	41, 42
37	ExprTuple	49, 57
38	Literal
39	ExprTuple	43, 44
40	ExprTuple	61
41	Operation	operator: 46 operands: 45
42	Operation	operator: 46 operands: 47
43	Variable
44	Operation	operator: 59 operands: 48
45	ExprTuple	49, 50
46	Literal
47	ExprTuple	54, 57
48	ExprTuple	61, 65
49	Operation	operator: 63 operands: 51
50	Operation	operator: 67 operand: 54
51	ExprTuple	53, 69
52	ExprTuple	54
53	Operation	operator: 67 operand: 57
54	Operation	operator: 63 operands: 56
55	ExprTuple	57
56	ExprTuple	58, 69
57	Operation	operator: 59 operands: 60
58	Variable
59	Literal
60	ExprTuple	61, 62
61	Literal
62	Operation	operator: 63 operands: 64
63	Literal
64	ExprTuple	65, 66
65	Literal
66	Operation	operator: 67 operand: 69
67	Literal
68	ExprTuple	69
69	Literal