Theorem fold_forall_natural_pos 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_pos

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

Passed sanity check: fold_forall_natural_pos 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(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()

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