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	reference	29	⊢
2	instantiation	5, 71, 78, 10, 6, 11, 13, 67, 14	⊢
	: , : , : , : , : , :
3	instantiation	51, 7, 8	⊢
	: , : , :
4	instantiation	58, 14	⊢
	:
5	theorem		⊢
	proveit.numbers.multiplication.disassociation
6	instantiation	16	⊢
	: , :
7	instantiation	9, 10, 78, 71, 11, 12, 13, 67, 14	⊢
	: , : , : , : , : , :
8	instantiation	59, 15	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.multiplication.association
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	16	⊢
	: , :
13	instantiation	17, 46, 67, 18	⊢
	: , :
14	instantiation	76, 69, 19	⊢
	: , : , :
15	instantiation	26, 20, 21	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17	theorem		⊢
	proveit.numbers.division.div_complex_closure
18	instantiation	22, 65	⊢
	:
19	instantiation	23, 24, 25	⊢
	: , : , :
20	instantiation	26, 27, 28	⊢
	: , : , :
21	instantiation	29, 30, 31, 32	⊢
	: , : , : , :
22	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
23	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
24	instantiation	33, 34	⊢
	: , :
25	assumption		⊢
26	theorem		⊢
	proveit.logic.equality.sub_right_side_into
27	instantiation	35, 46, 36, 37	⊢
	: , : , : , : , :
28	instantiation	51, 38, 39	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
30	instantiation	59, 40	⊢
	: , : , :
31	instantiation	59, 40	⊢
	: , : , :
32	instantiation	66, 46	⊢
	:
33	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
35	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
36	instantiation	76, 42, 41	⊢
	: , : , :
37	instantiation	76, 42, 43	⊢
	: , : , :
38	instantiation	59, 44	⊢
	: , : , :
39	instantiation	59, 45	⊢
	: , : , :
40	instantiation	61, 46	⊢
	:
41	instantiation	76, 48, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
43	instantiation	76, 48, 49	⊢
	: , : , :
44	instantiation	59, 50	⊢
	: , : , :
45	instantiation	51, 52, 53	⊢
	: , : , :
46	instantiation	76, 69, 54	⊢
	: , : , :
47	instantiation	76, 56, 55	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
49	instantiation	76, 56, 57	⊢
	: , : , :
50	instantiation	58, 67	⊢
	:
51	axiom		⊢
	proveit.logic.equality.equals_transitivity
52	instantiation	59, 60	⊢
	: , : , :
53	instantiation	61, 67	⊢
	:
54	instantiation	76, 72, 62	⊢
	: , : , :
55	instantiation	76, 64, 63	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
57	instantiation	76, 64, 65	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
59	axiom		⊢
	proveit.logic.equality.substitution
60	instantiation	66, 67	⊢
	:
61	theorem		⊢
	proveit.numbers.division.frac_one_denom
62	instantiation	76, 74, 68	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
66	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
67	instantiation	76, 69, 70	⊢
	: , : , :
68	instantiation	76, 77, 71	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
70	instantiation	76, 72, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
73	instantiation	76, 74, 75	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
75	instantiation	76, 77, 78	⊢
	: , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat2