Expression of type Lambda

from the theory of proveit.numbers.exponentiation

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 Exp, Integer, Natural

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(InSet(Exp(a, b), Integer), And(InSet(a, Integer), InSet(b, Natural))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 11 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 13 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 16
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Literal
11	ExprTuple	15, 17
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Variable
16	Literal
17	Variable
18	Literal