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