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Expression of type NotInSet

from the theory of proveit.physics.quantum.QPE

In [1]:
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 NotInSet
from proveit.numbers import Integer, frac, subtract
from proveit.physics.quantum.QPE import _delta_b, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = NotInSet(subtract(_delta_b, frac(l, _two_pow_t)), Integer)
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\delta_{b} - \frac{l}{2^{t}}\right) \notin \mathbb{Z}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operands: 6
4Literal
5Literal
6ExprTuple7, 8
7Operationoperator: 9
operand: 13
8Operationoperator: 11
operand: 14
9Literal
10ExprTuple13
11Literal
12ExprTuple14
13Variable
14Operationoperator: 15
operands: 16
15Literal
16ExprTuple17, 18
17Variable
18Operationoperator: 19
operands: 20
19Literal
20ExprTuple21, 22
21Literal
22Literal