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, e, l
from proveit.logic import And, 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(e, Conditional(Iff(And(InSet(l, Union(_neg_domain, _pos_domain)), sub_expr1), And(InSet(l, _full_domain), sub_expr1)).with_wrapping_at(1), InSet(e, _e_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(e \mapsto \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} \textrm{ if } e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}\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: 53 body: 3
2	ExprTuple	53
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	53, 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 41 operands: 15
12	ExprTuple	16, 18
13	Literal
14	ExprTuple	17, 18
15	ExprTuple	64, 19
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 58 operands: 25
20	ExprTuple	38, 26
21	Literal
22	ExprTuple	38, 27
23	Literal
24	ExprTuple	53, 28
25	ExprTuple	52, 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 41 operands: 32
28	Operation	operator: 33 operands: 34
29	Operation	operator: 62 operand: 56
30	Literal
31	ExprTuple	36, 37
32	ExprTuple	44, 52
33	Literal
34	ExprTuple	38, 39
35	ExprTuple	56
36	Operation	operator: 41 operands: 40
37	Operation	operator: 41 operands: 42
38	Variable
39	Operation	operator: 54 operands: 43
40	ExprTuple	44, 45
41	Literal
42	ExprTuple	49, 52
43	ExprTuple	56, 60
44	Operation	operator: 58 operands: 46
45	Operation	operator: 62 operand: 49
46	ExprTuple	48, 64
47	ExprTuple	49
48	Operation	operator: 62 operand: 52
49	Operation	operator: 58 operands: 51
50	ExprTuple	52
51	ExprTuple	53, 64
52	Operation	operator: 54 operands: 55
53	Variable
54	Literal
55	ExprTuple	56, 57
56	Literal
57	Operation	operator: 58 operands: 59
58	Literal
59	ExprTuple	60, 61
60	Literal
61	Operation	operator: 62 operand: 64
62	Literal
63	ExprTuple	64
64	Literal