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Expression of type LessEq

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 e, x
from proveit.numbers import Exp, Integrate, IntervalCC, LessEq, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
expr = LessEq(Integrate(index_or_indices = [x], integrand = frac(one, Exp(x, two)), domain = IntervalCC(e, subtract(_two_pow__t_minus_one, one))), frac(one, e))
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(\int_{e}^{2^{t - 1} - 1} \frac{1}{x^{2}}\,dx\right) \leq \frac{1}{e}
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: 13
operands: 7
5Literal
6ExprTuple8
7ExprTuple37, 23
8Lambdaparameter: 22
body: 10
9ExprTuple22
10Conditionalvalue: 11
condition: 12
11Operationoperator: 13
operands: 14
12Operationoperator: 15
operands: 16
13Literal
14ExprTuple37, 17
15Literal
16ExprTuple22, 18
17Operationoperator: 27
operands: 19
18Operationoperator: 20
operands: 21
19ExprTuple22, 29
20Literal
21ExprTuple23, 24
22Variable
23Variable
24Operationoperator: 31
operands: 25
25ExprTuple26, 34
26Operationoperator: 27
operands: 28
27Literal
28ExprTuple29, 30
29Literal
30Operationoperator: 31
operands: 32
31Literal
32ExprTuple33, 34
33Literal
34Operationoperator: 35
operand: 37
35Literal
36ExprTuple37
37Literal