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, 5, 6, 7, 8, 9, 10, 11^*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.association
2	reference	74	⊢
3	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
4	instantiation	12	⊢
	: , :
5	instantiation	12	⊢
	: , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	instantiation	15, 13, 14	⊢
	: , :
8	instantiation	15, 16, 17	⊢
	: , :
9	reference	37	⊢
10	instantiation	18, 30, 39, 19	⊢
	: , :
11	instantiation	20, 37, 30, 21, 22, 23^, 24^, 25^*	⊢
	: , : , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	instantiation	75, 48, 26	⊢
	: , : , :
14	instantiation	28, 30, 29	⊢
	: , :
15	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
16	instantiation	75, 48, 27	⊢
	: , : , :
17	instantiation	28, 29, 30	⊢
	: , :
18	theorem		⊢
	proveit.numbers.division.div_complex_closure
19	instantiation	31, 69	⊢
	:
20	theorem		⊢
	proveit.numbers.division.prod_of_fracs
21	instantiation	75, 33, 32	⊢
	: , : , :
22	instantiation	75, 33, 34	⊢
	: , : , :
23	instantiation	35, 37	⊢
	:
24	instantiation	36, 37	⊢
	:
25	instantiation	38, 39	⊢
	:
26	instantiation	75, 60, 40	⊢
	: , : , :
27	instantiation	75, 60, 41	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
29	instantiation	75, 48, 42	⊢
	: , : , :
30	instantiation	75, 48, 43	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
32	instantiation	75, 45, 44	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
34	instantiation	75, 45, 46	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.division.frac_one_denom
36	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
37	instantiation	75, 48, 47	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
39	instantiation	75, 48, 49	⊢
	: , : , :
40	instantiation	75, 71, 50	⊢
	: , : , :
41	instantiation	75, 71, 51	⊢
	: , : , :
42	instantiation	52, 53, 54	⊢
	: , : , :
43	instantiation	75, 60, 55	⊢
	: , : , :
44	instantiation	75, 57, 56	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
46	instantiation	75, 57, 58	⊢
	: , : , :
47	instantiation	75, 60, 59	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	75, 60, 61	⊢
	: , : , :
50	instantiation	75, 76, 62	⊢
	: , : , :
51	instantiation	75, 76, 63	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
53	instantiation	64, 65	⊢
	: , :
54	assumption		⊢
55	instantiation	75, 71, 66	⊢
	: , : , :
56	instantiation	75, 68, 67	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
58	instantiation	75, 68, 69	⊢
	: , : , :
59	instantiation	75, 71, 70	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
61	instantiation	75, 71, 72	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
64	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
66	instantiation	75, 76, 73	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
70	instantiation	75, 76, 74	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	instantiation	75, 76, 77	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
74	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
75	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
^*equality replacement requirements