Theorem add_nat_pos_from_nonneg of type Forall

from the theory of proveit.numbers.addition

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.addition import add_nat_pos_from_nonneg

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

Passed sanity check: add_nat_pos_from_nonneg matches stored_expr

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

\forall_{i, j \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{N}~|~b > 0}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \in \mathbb{N}^+\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	41, 44
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 19 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameters: 28 body: 13
11	Operation	operator: 46 operands: 14
12	Operation	operator: 46 operands: 15
13	Conditional	value: 16 condition: 17
14	ExprTuple	41, 50
15	ExprTuple	44, 50
16	Operation	operator: 46 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24, 25, 26
21	Operation	operator: 27 operands: 28
22	Literal
23	ExprRange	lambda_map: 29 start_index: 43 end_index: 41
24	Operation	operator: 46 operands: 30
25	ExprRange	lambda_map: 31 start_index: 43 end_index: 44
26	Operation	operator: 32 operands: 33
27	Literal
28	ExprTuple	34, 39, 35
29	Lambda	parameter: 54 body: 36
30	ExprTuple	39, 50
31	Lambda	parameter: 54 body: 37
32	Literal
33	ExprTuple	38, 39
34	ExprRange	lambda_map: 40 start_index: 43 end_index: 41
35	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
36	Operation	operator: 46 operands: 45
37	Operation	operator: 46 operands: 47
38	Literal
39	Variable
40	Lambda	parameter: 54 body: 48
41	Variable
42	Lambda	parameter: 54 body: 49
43	Literal
44	Variable
45	ExprTuple	48, 50
46	Literal
47	ExprTuple	49, 50
48	IndexedVar	variable: 51 index: 54
49	IndexedVar	variable: 52 index: 54
50	Literal
51	Variable
52	Variable
53	ExprTuple	54
54	Variable