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Expression of type Less

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.numbers import Exp, frac, greater, one, subtract, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor
In [2]:
# build up the expression from sub-expressions
expr = greater(frac(one, Exp(subtract(l, one), two)), frac(one, Exp(_diff_l_scaled_delta_floor, two)))
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())
\frac{1}{\left(l - 1\right)^{2}} > \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}
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)normalreversed('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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple24, 8
6Literal
7ExprTuple24, 9
8Operationoperator: 29
operands: 10
9Operationoperator: 29
operands: 11
10ExprTuple12, 33
11ExprTuple13, 33
12Operationoperator: 15
operands: 14
13Operationoperator: 15
operands: 16
14ExprTuple18, 17
15Literal
16ExprTuple18, 19
17Operationoperator: 21
operand: 23
18Variable
19Operationoperator: 21
operand: 24
20ExprTuple23
21Literal
22ExprTuple24
23Operationoperator: 25
operands: 26
24Literal
25Literal
26ExprTuple27, 28
27Operationoperator: 29
operands: 30
28Operationoperator: 31
operand: 35
29Literal
30ExprTuple33, 34
31Literal
32ExprTuple35
33Literal
34Literal
35Literal