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Expression of type And

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 And
from proveit.numbers import Less, LessEq, one, subtract, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor
In [2]:
# build up the expression from sub-expressions
sub_expr1 = subtract(l, one)
expr = And(LessEq(zero, sub_expr1), Less(sub_expr1, _diff_l_scaled_delta_floor))
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(0 \leq \left(l - 1\right)\right) \land \left(\left(l - 1\right) < \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)\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',)
as_total_orderingWhen 'True', style the conjunction as a total ordering (e.g. x < y < z from (x < y) and (y < z))NoneNone/False('with_total_ordering_style',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple10, 11
9Literal
10Operationoperator: 13
operands: 12
11Operationoperator: 13
operands: 14
12ExprTuple16, 15
13Literal
14ExprTuple16, 17
15Operationoperator: 19
operand: 21
16Variable
17Operationoperator: 19
operand: 22
18ExprTuple21
19Literal
20ExprTuple22
21Literal
22Operationoperator: 23
operands: 24
23Literal
24ExprTuple25, 26
25Operationoperator: 27
operands: 28
26Operationoperator: 29
operand: 33
27Literal
28ExprTuple31, 32
29Literal
30ExprTuple33
31Literal
32Literal
33Literal