# from the theory of proveit.numbers.number_sets.integers¶

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.
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, a
from proveit.logic import And, InSet
from proveit.numbers import Integer, NaturalPos, greater, zero
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(a, Conditional(InSet(a, NaturalPos), And(InSet(a, Integer), greater(a, zero)))))
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 \mapsto \left\{a \in \mathbb{N}^+ \textrm{ if } a \in \mathbb{Z} ,  a > 0\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 18
body: 3
2ExprTuple18
3Conditionalvalue: 4
condition: 5
4Operationoperator: 12
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple18, 9
7Literal
8ExprTuple10, 11
9Literal
10Operationoperator: 12
operands: 13
11Operationoperator: 14
operands: 15
12Literal
13ExprTuple18, 16
14Literal
15ExprTuple17, 18
16Literal
17Literal
18Variable