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Expression of type Implies

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 Forall, Implies, InSet
from proveit.numbers import Exp, Real, Sum, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, Real), domain = _neg_domain), InSet(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Real))
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[\forall_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}}~\left(\frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \in \mathbb{R}\right)\right] \Rightarrow \left(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) \in \mathbb{R}\right)
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
operand: 8
4Operationoperator: 23
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 18
8Lambdaparameter: 36
body: 10
9Operationoperator: 11
operand: 14
10Conditionalvalue: 13
condition: 20
11Literal
12ExprTuple14
13Operationoperator: 23
operands: 15
14Lambdaparameter: 36
body: 17
15ExprTuple19, 18
16ExprTuple36
17Conditionalvalue: 19
condition: 20
18Literal
19Operationoperator: 21
operands: 22
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple64, 25
23Literal
24ExprTuple36, 26
25Operationoperator: 52
operands: 27
26Operationoperator: 28
operands: 29
27ExprTuple30, 58
28Literal
29ExprTuple31, 32
30Operationoperator: 56
operands: 33
31Operationoperator: 56
operands: 34
32Operationoperator: 62
operand: 39
33ExprTuple36, 37
34ExprTuple38, 64
35ExprTuple39
36Variable
37Operationoperator: 62
operand: 43
38Operationoperator: 62
operand: 44
39Operationoperator: 56
operands: 42
40ExprTuple43
41ExprTuple44
42ExprTuple45, 64
43Operationoperator: 46
operands: 47
44Operationoperator: 52
operands: 48
45Variable
46Literal
47ExprTuple49, 50
48ExprTuple58, 51
49Operationoperator: 52
operands: 53
50Operationoperator: 54
operand: 59
51Operationoperator: 56
operands: 57
52Literal
53ExprTuple58, 60
54Literal
55ExprTuple59
56Literal
57ExprTuple60, 61
58Literal
59Literal
60Literal
61Operationoperator: 62
operand: 64
62Literal
63ExprTuple64
64Literal