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 Lambda, P, m, n
from proveit.logic import And, Forall, Implies
from proveit.numbers import NaturalPos, P_mAddOne, Pm, Pn, Pone

# build up the expression from sub-expressions
expr = Lambda(P, Implies(And(Pone, Forall(instance_param_or_params = [m], instance_expr = P_mAddOne, domain = NaturalPos, condition = Pm)), Forall(instance_param_or_params = [n], instance_expr = Pn, domain = NaturalPos)))

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())

P \mapsto \left(\left(P\left(1\right) \land \left[\forall_{m \in \mathbb{N}^+~|~P\left(m\right)}~P\left(m + 1\right)\right]\right) \Rightarrow \left[\forall_{n \in \mathbb{N}^+}~P\left(n\right)\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: 35 body: 2
1	ExprTuple	35
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 26 operands: 7
6	Operation	operator: 13 operand: 11
7	ExprTuple	9, 10
8	ExprTuple	11
9	Operation	operator: 35 operand: 37
10	Operation	operator: 13 operand: 16
11	Lambda	parameter: 24 body: 15
12	ExprTuple	37
13	Literal
14	ExprTuple	16
15	Conditional	value: 17 condition: 18
16	Lambda	parameter: 39 body: 19
17	Operation	operator: 35 operand: 24
18	Operation	operator: 33 operands: 21
19	Conditional	value: 22 condition: 23
20	ExprTuple	24
21	ExprTuple	24, 38
22	Operation	operator: 35 operand: 28
23	Operation	operator: 26 operands: 27
24	Variable
25	ExprTuple	28
26	Literal
27	ExprTuple	29, 30
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operand: 39
31	Literal
32	ExprTuple	39, 37
33	Literal
34	ExprTuple	39, 38
35	Variable
36	ExprTuple	39
37	Literal
38	Literal
39	Variable