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Expression of type Forall

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 a, b
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Mod
from proveit.physics.quantum.QPE import ModAdd, two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = Forall([a, b], Equals(ModAdd(a, b), Mod(Add(a, b), two_pow_t)), domain = Integer)
Out[2]:
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(expr.latex())
\forall_{a, b \in \mathbb{Z}}~\left(\left(a \oplus b\right) = \left(\left(a + b\right) ~\textup{mod}~ 2^{t}\right)\right)
In [5]:
expr.style_options()
Out[5]:
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 25
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13, 14
11Operationoperator: 15
operands: 25
12Operationoperator: 16
operands: 17
13Operationoperator: 19
operands: 18
14Operationoperator: 19
operands: 20
15Literal
16Literal
17ExprTuple21, 22
18ExprTuple28, 23
19Literal
20ExprTuple29, 23
21Operationoperator: 24
operands: 25
22Operationoperator: 26
operands: 27
23Literal
24Literal
25ExprTuple28, 29
26Literal
27ExprTuple30, 31
28Variable
29Variable
30Literal
31Literal