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, e, l
from proveit.logic import InSet, Union
from proveit.numbers import ModAbs, greater
from proveit.physics.quantum.QPE import _neg_domain, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(InSet(l, Union(_neg_domain, _pos_domain)), greater(ModAbs(l, _two_pow_t), e))

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 \in \left(\{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} \cup \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right), \left|l\right|_{\textup{mod}\thinspace 2^{t}} > e\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	15, 7
5	Literal
6	ExprTuple	30, 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	Variable
16	Operation	operator: 31 operands: 20
17	ExprTuple	21, 22
18	Literal
19	ExprTuple	26, 29
20	ExprTuple	33, 37
21	Operation	operator: 35 operands: 23
22	Operation	operator: 39 operand: 26
23	ExprTuple	25, 41
24	ExprTuple	26
25	Operation	operator: 39 operand: 29
26	Operation	operator: 35 operands: 28
27	ExprTuple	29
28	ExprTuple	30, 41
29	Operation	operator: 31 operands: 32
30	Variable
31	Literal
32	ExprTuple	33, 34
33	Literal
34	Operation	operator: 35 operands: 36
35	Literal
36	ExprTuple	37, 38
37	Literal
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Literal