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	⊢
	: , :
1	reference	42	⊢
2	instantiation	3, 4, 5, 6	⊢
	: , : , : , : , :
3	theorem		⊢
	proveit.core_expr_types.tuples.merge
4	instantiation	9, 7, 8	⊢
	:
5	instantiation	9, 10, 11	⊢
	:
6	instantiation	12	⊢
	:
7	instantiation	16, 13, 14	⊢
	: , :
8	instantiation	19, 15	⊢
	: , :
9	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
10	instantiation	16, 17, 18	⊢
	: , :
11	instantiation	19, 20	⊢
	: , :
12	axiom		⊢
	proveit.logic.equality.equals_reflexivity
13	instantiation	49, 25, 24	⊢
	: , : , :
14	instantiation	21, 22	⊢
	:
15	instantiation	23, 24	⊢
	:
16	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
17	instantiation	49, 25, 26	⊢
	: , : , :
18	instantiation	49, 27, 28	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
20	instantiation	29, 48, 30, 51, 31, 32*, 33*	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.negation.int_closure
22	instantiation	49, 34, 35	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
24	instantiation	37, 52, 36	⊢
	: , :
25	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
26	instantiation	37, 52, 55	⊢
	: , :
27	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
28	instantiation	38, 52	⊢
	:
29	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
31	instantiation	39, 40	⊢
	: , :
32	instantiation	41, 46	⊢
	:
33	instantiation	42, 43	⊢
	: , :
34	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
37	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
38	theorem		⊢
	proveit.numbers.negation.int_neg_closure
39	theorem		⊢
	proveit.numbers.ordering.relax_less
40	instantiation	44, 55	⊢
	:
41	theorem		⊢
	proveit.numbers.addition.elim_zero_left
42	theorem		⊢
	proveit.logic.equality.equals_reversal
43	instantiation	45, 46, 47	⊢
	: , :
44	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
45	theorem		⊢
	proveit.numbers.addition.commutation
46	instantiation	49, 50, 48	⊢
	: , : , :
47	instantiation	49, 50, 51	⊢
	: , : , :
48	instantiation	53, 54, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
51	instantiation	53, 54, 55	⊢
	: , : , :
52	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
53	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
54	instantiation	56, 57	⊢
	: , :
55	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
56	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements