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	⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.core_expr_types.tuples.merge
2	instantiation	7, 5, 6	⊢
	:
3	instantiation	7, 8, 9	⊢
	:
4	instantiation	10	⊢
	:
5	instantiation	14, 11, 12	⊢
	: , :
6	instantiation	17, 13	⊢
	: , :
7	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
8	instantiation	14, 15, 16	⊢
	: , :
9	instantiation	17, 18	⊢
	: , :
10	axiom		⊢
	proveit.logic.equality.equals_reflexivity
11	instantiation	42, 22, 21	⊢
	: , : , :
12	instantiation	42, 24, 19	⊢
	: , : , :
13	instantiation	20, 21	⊢
	:
14	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
15	instantiation	42, 22, 23	⊢
	: , : , :
16	instantiation	42, 24, 25	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
18	instantiation	26, 44, 27, 41, 28, 29*, 30*	⊢
	: , : , :
19	instantiation	33, 31	⊢
	:
20	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
21	instantiation	32, 48, 31	⊢
	: , :
22	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
23	instantiation	32, 48, 45	⊢
	: , :
24	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
25	instantiation	33, 48	⊢
	:
26	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
28	instantiation	34, 35	⊢
	: , :
29	instantiation	36, 39	⊢
	:
30	instantiation	37, 38, 39	⊢
	: , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
32	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
33	theorem		⊢
	proveit.numbers.negation.int_neg_closure
34	theorem		⊢
	proveit.numbers.ordering.relax_less
35	instantiation	40, 45	⊢
	:
36	theorem		⊢
	proveit.numbers.addition.elim_zero_left
37	theorem		⊢
	proveit.numbers.addition.commutation
38	instantiation	42, 43, 41	⊢
	: , : , :
39	instantiation	42, 43, 44	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
41	instantiation	46, 47, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	46, 47, 48	⊢
	: , : , :
45	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
46	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
47	instantiation	49, 50	⊢
	: , :
48	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
49	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements