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	23	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 55, 74, 72, 7^*	⊢
	: , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	50, 8	⊢
	:
6	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
7	instantiation	23, 9, 10	⊢
	: , : , :
8	instantiation	76, 61, 11	⊢
	: , : , :
9	instantiation	33, 34, 12, 13, 14, 15	⊢
	: , : , : , :
10	instantiation	16, 17, 18, 19, 20^, 21^	⊢
	: , : , :
11	instantiation	76, 69, 22	⊢
	: , : , :
12	instantiation	47	⊢
	: , :
13	instantiation	47	⊢
	: , :
14	instantiation	23, 24, 25	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.mult_6_3
16	theorem		⊢
	proveit.numbers.division.frac_cancel_left
17	instantiation	76, 27, 26	⊢
	: , : , :
18	instantiation	76, 27, 28	⊢
	: , : , :
19	instantiation	76, 61, 29	⊢
	: , : , :
20	instantiation	50, 30	⊢
	:
21	theorem		⊢
	proveit.numbers.numerals.decimals.mult_9_2
22	instantiation	76, 31, 32	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	33, 34, 35, 36, 37, 38	⊢
	: , : , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_6
26	instantiation	76, 40, 39	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
28	instantiation	76, 40, 41	⊢
	: , : , :
29	instantiation	76, 69, 42	⊢
	: , : , :
30	instantiation	76, 61, 43	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
32	instantiation	44, 45, 46	⊢
	: , :
33	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
35	instantiation	47	⊢
	: , :
36	instantiation	47	⊢
	: , :
37	instantiation	48, 49	⊢
	:
38	instantiation	50, 51	⊢
	:
39	instantiation	76, 53, 52	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
41	instantiation	76, 53, 54	⊢
	: , : , :
42	instantiation	76, 73, 55	⊢
	: , : , :
43	instantiation	76, 69, 56	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
45	instantiation	76, 58, 57	⊢
	: , : , :
46	instantiation	76, 58, 59	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
48	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
49	instantiation	76, 61, 60	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
51	instantiation	76, 61, 62	⊢
	: , : , :
52	instantiation	76, 64, 63	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
54	instantiation	76, 64, 65	⊢
	: , : , :
55	instantiation	76, 77, 66	⊢
	: , : , :
56	instantiation	76, 73, 67	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
60	instantiation	76, 69, 68	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
62	instantiation	76, 69, 70	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
67	instantiation	76, 77, 71	⊢
	: , : , :
68	instantiation	76, 73, 72	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
70	instantiation	76, 73, 74	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
72	instantiation	76, 77, 75	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
74	instantiation	76, 77, 78	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
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.nat6
^*equality replacement requirements