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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, Less, one, subtract, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor
In [2]:
# build up the expression from sub-expressions
expr = Less(Exp(subtract(l, one), two), 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())
\left(l - 1\right)^{2} < \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)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: 24
operands: 5
4Operationoperator: 24
operands: 6
5ExprTuple7, 28
6ExprTuple8, 28
7Operationoperator: 10
operands: 9
8Operationoperator: 10
operands: 11
9ExprTuple13, 12
10Literal
11ExprTuple13, 14
12Operationoperator: 16
operand: 18
13Variable
14Operationoperator: 16
operand: 19
15ExprTuple18
16Literal
17ExprTuple19
18Literal
19Operationoperator: 20
operands: 21
20Literal
21ExprTuple22, 23
22Operationoperator: 24
operands: 25
23Operationoperator: 26
operand: 30
24Literal
25ExprTuple28, 29
26Literal
27ExprTuple30
28Literal
29Literal
30Literal