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 Natural, P_mAddOne, Pm, Pn, Pzero

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

P \mapsto \left(\left(P\left(0\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: 36 body: 2
1	ExprTuple	36
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 27 operands: 7
6	Operation	operator: 13 operand: 11
7	ExprTuple	9, 10
8	ExprTuple	11
9	Operation	operator: 36 operand: 16
10	Operation	operator: 13 operand: 17
11	Lambda	parameter: 25 body: 15
12	ExprTuple	16
13	Literal
14	ExprTuple	17
15	Conditional	value: 18 condition: 19
16	Literal
17	Lambda	parameter: 40 body: 20
18	Operation	operator: 36 operand: 25
19	Operation	operator: 34 operands: 22
20	Conditional	value: 23 condition: 24
21	ExprTuple	25
22	ExprTuple	25, 39
23	Operation	operator: 36 operand: 29
24	Operation	operator: 27 operands: 28
25	Variable
26	ExprTuple	29
27	Literal
28	ExprTuple	30, 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 36 operand: 40
32	Literal
33	ExprTuple	40, 38
34	Literal
35	ExprTuple	40, 39
36	Variable
37	ExprTuple	40
38	Literal
39	Literal
40	Variable