Theorem fold_forall_natural of type Forall

from the theory of proveit.numbers.number_sets.natural_numbers

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.number_sets.natural_numbers import fold_forall_natural

# check that the built expression is the same as the stored expression
assert fold_forall_natural.expr == stored_expr
assert fold_forall_natural.expr._style_id == stored_expr._style_id
print("Passed sanity check: fold_forall_natural matches stored_expr")

Passed sanity check: fold_forall_natural matches stored_expr

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

\forall_{P}~\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()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 15 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 38 body: 4
3	ExprTuple	38
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 29 operands: 9
8	Operation	operator: 15 operand: 13
9	ExprTuple	11, 12
10	ExprTuple	13
11	Operation	operator: 38 operand: 18
12	Operation	operator: 15 operand: 19
13	Lambda	parameter: 27 body: 17
14	ExprTuple	18
15	Literal
16	ExprTuple	19
17	Conditional	value: 20 condition: 21
18	Literal
19	Lambda	parameter: 42 body: 22
20	Operation	operator: 38 operand: 27
21	Operation	operator: 36 operands: 24
22	Conditional	value: 25 condition: 26
23	ExprTuple	27
24	ExprTuple	27, 41
25	Operation	operator: 38 operand: 31
26	Operation	operator: 29 operands: 30
27	Variable
28	ExprTuple	31
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operand: 42
34	Literal
35	ExprTuple	42, 40
36	Literal
37	ExprTuple	42, 41
38	Variable
39	ExprTuple	42
40	Literal
41	Literal
42	Variable