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, 4, 5, 6*	,  ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	instantiation	30, 20, 7	⊢
	: , : , :
3	reference	10	⊢
4	instantiation	8, 11, 12	⊢
	: , :
5	instantiation	9, 10, 11, 12, 13, 14	,  ⊢
	: , : , :
6	instantiation	15, 16, 17	⊢
	: , : , :
7	instantiation	30, 27, 18	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
9	theorem		⊢
	proveit.numbers.ordering.less_add_right
10	assumption		⊢
11	instantiation	30, 20, 19	⊢
	: , : , :
12	instantiation	30, 20, 21	⊢
	: , : , :
13	assumption		⊢
14	instantiation	22, 32	⊢
	:
15	axiom		⊢
	proveit.logic.equality.equals_transitivity
16	instantiation	23, 24	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_3
18	instantiation	30, 31, 25	⊢
	: , : , :
19	instantiation	30, 27, 26	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
21	instantiation	30, 27, 28	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
23	axiom		⊢
	proveit.logic.equality.substitution
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
26	instantiation	30, 31, 29	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
28	instantiation	30, 31, 32	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
30	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
31	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements