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, 12^*	, , , ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.association
2	reference	61	⊢
3	instantiation	13	⊢
	: , :
4	instantiation	13	⊢
	: , :
5	instantiation	13	⊢
	: , :
6	instantiation	14, 15, 16	⊢
	: , :
7	instantiation	70, 51, 17	⊢
	: , : , :
8	reference	40	⊢
9	instantiation	18, 23, 42, 19	⊢
	: , :
10	instantiation	70, 51, 20	⊢
	: , : , :
11	instantiation	70, 51, 21	⊢
	: , : , :
12	instantiation	22, 40, 23, 24, 25, 26^, 27^, 28^*	⊢
	: , : , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
15	instantiation	70, 51, 29	⊢
	: , : , :
16	instantiation	70, 51, 30	⊢
	: , : , :
17	instantiation	70, 43, 31	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.division.div_complex_closure
19	instantiation	32, 65	⊢
	:
20	instantiation	70, 43, 33	⊢
	: , : , :
21	assumption		⊢
22	theorem		⊢
	proveit.numbers.division.prod_of_fracs
23	instantiation	70, 51, 34	⊢
	: , : , :
24	instantiation	70, 36, 35	⊢
	: , : , :
25	instantiation	70, 36, 37	⊢
	: , : , :
26	instantiation	38, 40	⊢
	:
27	instantiation	39, 40	⊢
	:
28	instantiation	41, 42	⊢
	:
29	instantiation	70, 43, 44	⊢
	: , : , :
30	instantiation	70, 59, 45	⊢
	: , : , :
31	assumption		⊢
32	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
33	assumption		⊢
34	instantiation	70, 59, 46	⊢
	: , : , :
35	instantiation	70, 48, 47	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
37	instantiation	70, 48, 49	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.division.frac_one_denom
39	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
40	instantiation	70, 51, 50	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
42	instantiation	70, 51, 52	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
44	assumption		⊢
45	instantiation	70, 67, 53	⊢
	: , : , :
46	instantiation	70, 67, 54	⊢
	: , : , :
47	instantiation	70, 56, 55	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
49	instantiation	70, 56, 57	⊢
	: , : , :
50	instantiation	70, 59, 58	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
52	instantiation	70, 59, 60	⊢
	: , : , :
53	instantiation	70, 71, 61	⊢
	: , : , :
54	instantiation	70, 71, 62	⊢
	: , : , :
55	instantiation	70, 64, 63	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
57	instantiation	70, 64, 65	⊢
	: , : , :
58	instantiation	70, 67, 66	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	70, 67, 68	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
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.posnat3
66	instantiation	70, 71, 69	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
68	instantiation	70, 71, 72	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
70	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
71	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements