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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 b, l
from proveit.logic import Forall, NotEquals, Set
from proveit.numbers import Integer, Mult, zero
from proveit.physics.quantum.QPE import _b_floor, _b_round, _delta_b, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [b, l], instance_expr = NotEquals(Mult(_two_pow_t, _delta_b), l), domains = [Set(_b_floor, _b_round), Integer], condition = NotEquals(l, zero))
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())
\forall_{b \in \left\{b_{\textit{f}}, b_{\textit{r}}\right\}, l \in \mathbb{Z}~|~l \neq 0}~\left(\left(2^{t} \cdot \delta_{b}\right) \neq l\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
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
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple36, 26
5Conditionalvalue: 6
condition: 7
6Operationoperator: 20
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 26
9Literal
10ExprTuple12, 13, 14
11Operationoperator: 15
operands: 16
12Operationoperator: 18
operands: 17
13Operationoperator: 18
operands: 19
14Operationoperator: 20
operands: 21
15Literal
16ExprTuple22, 23
17ExprTuple36, 24
18Literal
19ExprTuple26, 25
20Literal
21ExprTuple26, 27
22Operationoperator: 28
operands: 29
23Operationoperator: 30
operand: 36
24Operationoperator: 32
operands: 33
25Literal
26Variable
27Literal
28Literal
29ExprTuple34, 35
30Literal
31ExprTuple36
32Literal
33ExprTuple37, 38
34Literal
35Literal
36Variable
37Literal
38Literal