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	⊢
	: , : , :
1	reference	31	⊢
2	instantiation	31, 4, 5	⊢
	: , : , :
3	instantiation	31, 6, 7	⊢
	: , : , :
4	instantiation	9, 8	⊢
	: , : , :
5	instantiation	9, 10	⊢
	: , : , :
6	instantiation	11, 12, 14	⊢
	: , :
7	instantiation	13, 19, 14, 15^*	⊢
	: , :
8	instantiation	16, 26, 27, 28	⊢
	: , :
9	axiom		⊢
	proveit.logic.equality.substitution
10	instantiation	17, 23, 20, 21	⊢
	: , :
11	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
12	instantiation	18, 19	⊢
	:
13	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left_double
14	instantiation	25, 23, 20, 21	⊢
	: , :
15	instantiation	22, 26, 23, 44, 45, 24^*	⊢
	: , : , : , :
16	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
17	theorem		⊢
	proveit.numbers.division.neg_frac_neg_denominator
18	theorem		⊢
	proveit.numbers.negation.complex_closure
19	instantiation	25, 26, 27, 28	⊢
	: , :
20	instantiation	78, 57, 29	⊢
	: , : , :
21	instantiation	36, 77	⊢
	:
22	theorem		⊢
	proveit.numbers.division.prod_of_fracs
23	instantiation	78, 57, 30	⊢
	: , : , :
24	instantiation	31, 32, 33	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.division.div_complex_closure
26	instantiation	78, 57, 34	⊢
	: , : , :
27	instantiation	78, 57, 35	⊢
	: , : , :
28	instantiation	36, 75	⊢
	:
29	instantiation	78, 66, 37	⊢
	: , : , :
30	instantiation	78, 66, 38	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	39, 68, 40, 41, 42, 48	⊢
	: , : , : , :
33	instantiation	43, 44, 45, 46, 47^, 48^	⊢
	: , : , :
34	instantiation	78, 66, 49	⊢
	: , : , :
35	instantiation	78, 66, 50	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
37	instantiation	78, 73, 51	⊢
	: , : , :
38	instantiation	78, 73, 52	⊢
	: , : , :
39	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
40	instantiation	53	⊢
	: , :
41	instantiation	53	⊢
	: , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_6
43	theorem		⊢
	proveit.numbers.division.frac_cancel_left
44	instantiation	78, 55, 54	⊢
	: , : , :
45	instantiation	78, 55, 56	⊢
	: , : , :
46	instantiation	78, 57, 58	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_4
48	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_5
49	instantiation	78, 73, 59	⊢
	: , : , :
50	instantiation	78, 73, 60	⊢
	: , : , :
51	instantiation	78, 79, 61	⊢
	: , : , :
52	instantiation	78, 79, 62	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
54	instantiation	78, 64, 63	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
56	instantiation	78, 64, 65	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
58	instantiation	78, 66, 67	⊢
	: , : , :
59	instantiation	78, 79, 68	⊢
	: , : , :
60	instantiation	78, 79, 69	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
63	instantiation	78, 71, 70	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
65	instantiation	78, 71, 72	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
67	instantiation	78, 73, 74	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
70	instantiation	78, 76, 75	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
72	instantiation	78, 76, 77	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
74	instantiation	78, 79, 80	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
78	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements