Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3	,  ⊢
	: , :
1	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
2	instantiation	4, 38, 5	,  ⊢
	:
3	instantiation	46, 6, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
5	instantiation	8, 9, 41, 10, 11, 12*, 13*	,  ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
7	instantiation	46, 14, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
9	instantiation	16, 41	⊢
	:
10	instantiation	17, 38, 41	⊢
	: , :
11	instantiation	18, 41, 38, 19, 20	,  ⊢
	: , : , :
12	instantiation	21, 37, 34	⊢
	: , :
13	instantiation	22, 23, 24	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
15	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
16	theorem		⊢
	proveit.numbers.negation.real_closure
17	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
18	theorem		⊢
	proveit.numbers.ordering.less_add_right
19	assumption		⊢
20	instantiation	25, 48	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	26, 27, 48, 28, 29, 30, 33, 37, 31	⊢
	: , : , : , : , : , :
24	instantiation	32, 37, 33, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
26	theorem		⊢
	proveit.numbers.addition.disassociation
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	instantiation	35	⊢
	: , :
31	instantiation	36, 37	⊢
	:
32	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
33	instantiation	46, 40, 38	⊢
	: , : , :
34	instantiation	39	⊢
	:
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	theorem		⊢
	proveit.numbers.negation.complex_closure
37	instantiation	46, 40, 41	⊢
	: , : , :
38	assumption		⊢
39	axiom		⊢
	proveit.logic.equality.equals_reflexivity
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	46, 42, 43	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	46, 44, 45	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
45	instantiation	46, 47, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements