Expression of type Or

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 l
from proveit.logic import InSet, Or
from proveit.physics.quantum.QPE import _neg_domain, _pos_domain

# build up the expression from sub-expressions
expr = Or(InSet(l, _neg_domain), InSet(l, _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(l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right) \lor \left(l \in \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	9, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 12 operands: 11
9	Variable
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	19, 22
14	Operation	operator: 28 operands: 16
15	Operation	operator: 32 operand: 19
16	ExprTuple	18, 34
17	ExprTuple	19
18	Operation	operator: 32 operand: 22
19	Operation	operator: 28 operands: 21
20	ExprTuple	22
21	ExprTuple	23, 34
22	Operation	operator: 24 operands: 25
23	Variable
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Literal
31	Operation	operator: 32 operand: 34
32	Literal
33	ExprTuple	34
34	Literal