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*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.summation.trivial_sum
2	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
3	instantiation	6, 7, 47	⊢
	: , :
4	reference	32	⊢
5	instantiation	13, 8, 9	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
7	instantiation	53, 10, 46	⊢
	: , : , :
8	instantiation	16, 11	⊢
	: , : , :
9	instantiation	12, 33	⊢
	:
10	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
11	instantiation	13, 14, 15	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	16, 17	⊢
	: , : , :
15	instantiation	18, 19, 20, 21	⊢
	: , : , : , :
16	axiom		⊢
	proveit.logic.equality.substitution
17	theorem		⊢
	proveit.numbers.negation.negated_zero
18	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
19	instantiation	22, 23, 28, 24, 29, 25, 33, 30, 26, 32	⊢
	: , : , : , : , : , :
20	instantiation	27, 28, 55, 29, 33, 30, 32	⊢
	: , : , : , :
21	instantiation	31, 32, 33, 34	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.addition.disassociation
23	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	instantiation	35	⊢
	: , :
26	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
27	theorem		⊢
	proveit.numbers.addition.elim_zero_any
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
29	instantiation	35	⊢
	: , :
30	instantiation	53, 38, 36	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
32	instantiation	53, 38, 37	⊢
	: , : , :
33	instantiation	53, 38, 39	⊢
	: , : , :
34	instantiation	40	⊢
	:
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	instantiation	53, 42, 41	⊢
	: , : , :
37	instantiation	53, 42, 43	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
39	instantiation	44, 45, 46	⊢
	: , : , :
40	axiom		⊢
	proveit.logic.equality.equals_reflexivity
41	instantiation	53, 48, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	53, 48, 52	⊢
	: , : , :
44	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
45	instantiation	49, 50	⊢
	: , :
46	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
47	instantiation	51, 52	⊢
	:
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
51	theorem		⊢
	proveit.numbers.negation.int_closure
52	instantiation	53, 54, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements