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, Lambda, a, b
from proveit.logic import And, InSet
from proveit.numbers import Mult, Natural

In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(InSet(Mult(a, b), Natural), And(InSet(a, Natural), InSet(b, Natural))))

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(a, b\right) \mapsto \left\{\left(a \cdot b\right) \in \mathbb{N} \textrm{ if } a \in \mathbb{N} ,  b \in \mathbb{N}\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 11
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 13
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 17
5Literal
6ExprTuple8, 9
7Operationoperator: 10
operands: 11
8Operationoperator: 13
operands: 12
9Operationoperator: 13
operands: 14
10Literal
11ExprTuple15, 16
12ExprTuple15, 17
13Literal
14ExprTuple16, 17
15Variable
16Variable
17Literal