Expression of type Lambda

from the theory of proveit.numbers.number_sets.natural_numbers

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, m, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Natural, one

# build up the expression from sub-expressions
expr = Lambda([m, n], Conditional(Equals(n, m), And(InSet(m, Natural), InSet(n, Natural), Equals(Add(m, one), Add(n, one)))))

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(m, n\right) \mapsto \left\{n = m \textrm{ if } m \in \mathbb{N} ,  n \in \mathbb{N} ,  \left(m + 1\right) = \left(n + 1\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	22, 23
2	Conditional	value: 3 condition: 4
3	Operation	operator: 14 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	23, 22
6	Literal
7	ExprTuple	8, 9, 10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	22, 16
12	Literal
13	ExprTuple	23, 16
14	Literal
15	ExprTuple	17, 18
16	Literal
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 24
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Variable
24	Literal