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Expression of type Conditional

from the theory of proveit.numbers.modular

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 Conditional, a, b
from proveit.logic import And, Equals, InSet
from proveit.numbers import Mod, Real, RealPos
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mod(a, b)
expr = Conditional(Equals(Mod(sub_expr1, b), sub_expr1), And(InSet(a, Real), InSet(b, RealPos)))
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\{\left(\left(a ~\textup{mod}~ b\right) ~\textup{mod}~ b\right) = \left(a ~\textup{mod}~ b\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R}^+\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 14
5Literal
6ExprTuple8, 9
7Operationoperator: 17
operands: 10
8Operationoperator: 12
operands: 11
9Operationoperator: 12
operands: 13
10ExprTuple14, 20
11ExprTuple19, 15
12Literal
13ExprTuple20, 16
14Operationoperator: 17
operands: 18
15Literal
16Literal
17Literal
18ExprTuple19, 20
19Variable
20Variable