# 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, Lambda, a, b, n
from proveit.logic import And, Forall, InSet
from proveit.numbers import Integer, Interval, LessEq

In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Forall(instance_param_or_params = [n], instance_expr = LessEq(n, b), domain = Interval(a, b)), And(InSet(a, Integer), InSet(b, Integer))))

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\{\forall_{n \in \{a~\ldotp \ldotp~b\}}~\left(n \leq b\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z}\right..

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0Lambdaparameters: 25
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operand: 8
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8
6Literal
7ExprTuple9, 10
8Lambdaparameter: 22
body: 12
9Operationoperator: 20
operands: 13
10Operationoperator: 20
operands: 14
11ExprTuple22
12Conditionalvalue: 15
condition: 16
13ExprTuple26, 17
14ExprTuple27, 17
15Operationoperator: 18
operands: 19
16Operationoperator: 20
operands: 21
17Literal
18Literal
19ExprTuple22, 27
20Literal
21ExprTuple22, 23
22Variable
23Operationoperator: 24
operands: 25
24Literal
25ExprTuple26, 27
26Variable
27Variable