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	reference	22	⊢
2	instantiation	34, 7, 4, 6, 5	, , , , , , ,  ⊢
	: , : , :
3	instantiation	31, 6, 7, 8, 9	, , , , , ,  ⊢
	: , : , :
4	instantiation	15, 10, 14	, ,  ⊢
	: , :
5	instantiation	16, 14, 10, 13, 11, 12	, , , , , ,  ⊢
	: , : , :
6	instantiation	15, 13, 14	, , ,  ⊢
	: , :
7	instantiation	15, 18, 17	, ,  ⊢
	: , :
8	instantiation	15, 19, 17	, ,  ⊢
	: , :
9	instantiation	16, 17, 18, 19, 20, 21	, , , ,  ⊢
	: , : , :
10	instantiation	26, 32, 36	,  ⊢
	: , :
11	instantiation	22, 23, 24	, , , , ,  ⊢
	: , : , :
12	instantiation	29, 25	,  ⊢
	:
13	instantiation	26, 35, 37	,  ⊢
	: , :
14	instantiation	45, 46, 25	,  ⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
16	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_left_factor_bound
17	instantiation	45, 46, 30	,  ⊢
	: , : , :
18	instantiation	26, 36, 28	,  ⊢
	: , :
19	instantiation	45, 46, 27	,  ⊢
	: , : , :
20	instantiation	31, 28, 36, 37, 38	, , ,  ⊢
	: , : , :
21	instantiation	29, 30	,  ⊢
	:
22	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
23	instantiation	31, 36, 32, 35, 33	, , ,  ⊢
	: , : , :
24	instantiation	34, 35, 36, 37, 38	, , ,  ⊢
	: , : , :
25	instantiation	39, 41, 42	,  ⊢
	: , :
26	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
27	instantiation	39, 47, 40	,  ⊢
	: , :
28	instantiation	45, 46, 40	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
30	instantiation	39, 40, 41	,  ⊢
	: , :
31	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
32	instantiation	45, 46, 42	⊢
	: , : , :
33	assumption		⊢
34	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
35	instantiation	45, 46, 43	⊢
	: , : , :
36	instantiation	45, 46, 44	⊢
	: , : , :
37	instantiation	45, 46, 47	⊢
	: , : , :
38	assumption		⊢
39	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
40	assumption		⊢
41	assumption		⊢
42	assumption		⊢
43	assumption		⊢
44	assumption		⊢
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
47	assumption		⊢