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