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
from proveit.logic import And, InSet
from proveit.numbers import NaturalPos, P_mAddOne, Pm

# build up the expression from sub-expressions
expr = Lambda(m, Conditional(P_mAddOne, And(InSet(m, NaturalPos), Pm)))

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())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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