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 And, InSet, Union
from proveit.numbers import Less, ModAbs, greater, zero
from proveit.physics.quantum.QPE import _neg_domain, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Less(l, zero), And(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 < 0, \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)

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: 11 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	21, 6
4	Literal
5	ExprTuple	7, 8
6	Literal
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	21, 13
11	Literal
12	ExprTuple	36, 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 24 operands: 23
20	Operation	operator: 24 operands: 25
21	Variable
22	Operation	operator: 37 operands: 26
23	ExprTuple	27, 28
24	Literal
25	ExprTuple	32, 35
26	ExprTuple	39, 43
27	Operation	operator: 41 operands: 29
28	Operation	operator: 45 operand: 32
29	ExprTuple	31, 47
30	ExprTuple	32
31	Operation	operator: 45 operand: 35
32	Operation	operator: 41 operands: 34
33	ExprTuple	35
34	ExprTuple	36, 47
35	Operation	operator: 37 operands: 38
36	Variable
37	Literal
38	ExprTuple	39, 40
39	Literal
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Literal
44	Operation	operator: 45 operand: 47
45	Literal
46	ExprTuple	47
47	Literal