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