Show the Proof¶

In [1]:

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

Out[1]:

	step type	requirements	statement
0	instantiation	1, 2, 3, 4	, , ⊢
	: , : , : , :
1	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	instantiation	5, 64, 74, 11, 6, 13, 14, 7, 8, 16	, , ⊢
	: , : , : , : , : , :
3	instantiation	61, 9	⊢
	: , : , :
4	instantiation	10, 64, 74, 11, 12, 13, 14, 15, 43, 16	, , ⊢
	: , : , : , : , : , :
5	theorem		⊢
	proveit.numbers.multiplication.association
6	instantiation	20	⊢
	: , :
7	instantiation	21, 72, 22, 23	⊢
	: , :
8	instantiation	21, 43, 72, 17	⊢
	: , :
9	instantiation	27, 18, 19	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.multiplication.disassociation
11	instantiation	20	⊢
	: , :
12	instantiation	20	⊢
	: , :
13	assumption		⊢
14	assumption		⊢
15	instantiation	21, 35, 22, 23	⊢
	: , :
16	instantiation	24, 25, 26	⊢
	: , :
17	instantiation	32, 75	⊢
	:
18	instantiation	27, 28, 29	⊢
	: , : , :
19	instantiation	61, 30	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21	theorem		⊢
	proveit.numbers.division.div_complex_closure
22	instantiation	86, 79, 31	⊢
	: , : , :
23	instantiation	32, 76	⊢
	:
24	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
25	assumption		⊢
26	instantiation	86, 79, 33	⊢
	: , : , :
27	theorem		⊢
	proveit.logic.equality.sub_right_side_into
28	instantiation	34, 35, 43, 36, 37, 38	⊢
	: , : , : , : , :
29	instantiation	39, 40, 41	⊢
	: , : , :
30	instantiation	42, 43	⊢
	:
31	instantiation	86, 82, 44	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
33	instantiation	45, 46	⊢
	:
34	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
35	instantiation	86, 79, 46	⊢
	: , : , :
36	instantiation	86, 49, 47	⊢
	: , : , :
37	instantiation	86, 49, 48	⊢
	: , : , :
38	instantiation	86, 49, 50	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.equals_transitivity
40	instantiation	61, 51	⊢
	: , : , :
41	instantiation	61, 52	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.division.frac_one_denom
43	instantiation	86, 79, 53	⊢
	: , : , :
44	instantiation	86, 84, 54	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.negation.real_closure
46	instantiation	86, 82, 55	⊢
	: , : , :
47	instantiation	86, 58, 56	⊢
	: , : , :
48	instantiation	86, 58, 57	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
50	instantiation	86, 58, 59	⊢
	: , : , :
51	instantiation	61, 60	⊢
	: , : , :
52	instantiation	61, 62	⊢
	: , : , :
53	instantiation	86, 82, 63	⊢
	: , : , :
54	instantiation	86, 87, 64	⊢
	: , : , :
55	instantiation	86, 84, 65	⊢
	: , : , :
56	instantiation	86, 68, 66	⊢
	: , : , :
57	instantiation	86, 68, 67	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
59	instantiation	86, 68, 69	⊢
	: , : , :
60	instantiation	70, 72	⊢
	:
61	axiom		⊢
	proveit.logic.equality.substitution
62	instantiation	71, 72	⊢
	:
63	instantiation	86, 84, 73	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
65	instantiation	86, 87, 74	⊢
	: , : , :
66	instantiation	86, 77, 75	⊢
	: , : , :
67	instantiation	86, 77, 76	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
69	instantiation	86, 77, 78	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
71	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
72	instantiation	86, 79, 80	⊢
	: , : , :
73	instantiation	86, 87, 81	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
75	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
79	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
80	instantiation	86, 82, 83	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
83	instantiation	86, 84, 85	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
85	instantiation	86, 87, 88	⊢
	: , : , :
86	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat3