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