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Expression of type Conditional

from the theory of proveit.numbers.multiplication

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, InSet
from proveit.numbers import IntegerNonPos, Mult, Natural
In [2]:
# build up the expression from sub-expressions
expr = Conditional(InSet(Mult(a, b), Natural), And(InSet(a, IntegerNonPos), InSet(b, IntegerNonPos)))
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(a \cdot b\right) \in \mathbb{N} \textrm{ if } a \in \mathbb{Z}^{\leq 0} ,  b \in \mathbb{Z}^{\leq 0}\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: 13
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8, 9
6Operationoperator: 10
operands: 11
7Literal
8Operationoperator: 13
operands: 12
9Operationoperator: 13
operands: 14
10Literal
11ExprTuple15, 16
12ExprTuple15, 17
13Literal
14ExprTuple16, 17
15Variable
16Variable
17Literal