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	53	⊢
2	instantiation	65, 3, 4	, , ,  ⊢
	: , : , :
3	instantiation	50, 5	⊢
	: , : , :
4	instantiation	6, 7, 8, 9	, , ,  ⊢
	: , : , : , :
5	instantiation	50, 10	⊢
	: , : , :
6	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
7	instantiation	11, 12, 120, 13, 75, 17, 68, 22, 23	, , ,  ⊢
	: , : , : , : , : , : , :
8	instantiation	19, 56, 115, 14, 57, 15, 16, 75, 17, 68, 22, 23, 18*	, , ,  ⊢
	: , : , : , : , : , :
9	instantiation	19, 120, 115, 20, 21, 29, 68, 22, 23, 24*	, , ,  ⊢
	: , : , : , : , : , :
10	instantiation	25, 75, 93, 89, 26*	⊢
	: , :
11	theorem		⊢
	proveit.numbers.addition.leftward_commutation
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
13	instantiation	27	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
15	instantiation	91	⊢
	: , :
16	instantiation	28	⊢
	: , : , : , :
17	instantiation	73, 29	⊢
	:
18	instantiation	65, 30, 31, 32*	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.association
20	instantiation	91	⊢
	: , :
21	instantiation	91	⊢
	: , :
22	instantiation	118, 108, 33	⊢
	: , : , :
23	instantiation	38, 93, 34	⊢
	: , :
24	instantiation	53, 35, 83*	⊢
	: , :
25	theorem		⊢
	proveit.numbers.division.div_as_mult
26	instantiation	65, 36, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
29	instantiation	38, 74, 75	⊢
	: , :
30	instantiation	50, 39	⊢
	: , : , :
31	instantiation	53, 40	⊢
	: , :
32	instantiation	41, 117, 42, 112, 43*, 44*, 45*	⊢
	: , : , : , :
33	instantiation	118, 100, 46	⊢
	: , : , :
34	instantiation	118, 108, 47	⊢
	: , : , :
35	instantiation	55, 56, 115, 120, 57, 48, 104, 68, 49*	⊢
	: , : , : , : , : , :
36	instantiation	50, 51	⊢
	: , : , :
37	instantiation	52, 75, 74	⊢
	: , :
38	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
39	instantiation	53, 54	⊢
	: , :
40	instantiation	55, 56, 115, 120, 57, 58, 104, 59, 75, 60*	⊢
	: , : , : , : , : , :
41	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
42	instantiation	61, 117	⊢
	:
43	instantiation	62, 104, 63	⊢
	:
44	instantiation	64, 104, 93, 89	⊢
	: , :
45	instantiation	65, 66, 67	⊢
	: , : , :
46	assumption		⊢
47	assumption		⊢
48	instantiation	91	⊢
	: , :
49	instantiation	92, 68	⊢
	:
50	axiom		⊢
	proveit.logic.equality.substitution
51	instantiation	69, 70, 76, 71*	⊢
	: , :
52	theorem		⊢
	proveit.numbers.multiplication.commutation
53	theorem		⊢
	proveit.logic.equality.equals_reversal
54	instantiation	72, 74, 75	⊢
	: , :
55	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
56	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
57	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
58	instantiation	91	⊢
	: , :
59	instantiation	73, 74	⊢
	:
60	instantiation	92, 75	⊢
	:
61	theorem		⊢
	proveit.numbers.negation.int_closure
62	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
63	instantiation	99, 76	⊢
	:
64	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
65	axiom		⊢
	proveit.logic.equality.equals_transitivity
66	instantiation	77, 115, 78, 79, 80, 81	⊢
	: , : , : , :
67	instantiation	82, 104, 93, 83	⊢
	: , : , :
68	instantiation	118, 108, 84	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
70	instantiation	118, 85, 86	⊢
	: , : , :
71	instantiation	87, 93	⊢
	:
72	theorem		⊢
	proveit.numbers.negation.neg_times_pos
73	theorem		⊢
	proveit.numbers.negation.complex_closure
74	instantiation	88, 104, 93, 89	⊢
	: , :
75	instantiation	118, 108, 90	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
77	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
78	instantiation	91	⊢
	: , :
79	instantiation	91	⊢
	: , :
80	instantiation	92, 93	⊢
	:
81	instantiation	94, 104, 95*	⊢
	: , :
82	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
83	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
84	instantiation	118, 100, 96	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
86	instantiation	118, 97, 98	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
88	theorem		⊢
	proveit.numbers.division.div_complex_closure
89	instantiation	99, 111	⊢
	:
90	instantiation	118, 100, 101	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
92	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
93	instantiation	118, 108, 102	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.negation.pos_times_neg
95	instantiation	103, 104	⊢
	:
96	assumption		⊢
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
98	instantiation	118, 105, 106	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
101	assumption		⊢
102	instantiation	118, 113, 107	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
104	instantiation	118, 108, 109	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
106	instantiation	118, 110, 111	⊢
	: , : , :
107	instantiation	118, 116, 112	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
109	instantiation	118, 113, 114	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
111	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
112	instantiation	118, 119, 115	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
114	instantiation	118, 116, 117	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
116	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
117	instantiation	118, 119, 120	⊢
	: , : , :
118	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
119	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
120	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements