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.multiplication.strong_bound_via_left_factor_bound
2	instantiation	17, 18, 14	,  ⊢
	: , : , :
3	instantiation	7, 9, 10	,  ⊢
	: , :
4	instantiation	7, 9, 11	,  ⊢
	: , :
5	instantiation	8, 9, 10, 11, 12	, , ,  ⊢
	: , : , :
6	instantiation	13, 14	,  ⊢
	:
7	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
8	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
9	instantiation	17, 18, 15	⊢
	: , : , :
10	instantiation	17, 18, 16	⊢
	: , : , :
11	instantiation	17, 18, 19	⊢
	: , : , :
12	assumption		⊢
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
14	instantiation	20, 21, 22	,  ⊢
	: , :
15	assumption		⊢
16	assumption		⊢
17	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
19	assumption		⊢
20	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
21	assumption		⊢
22	assumption		⊢