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	17	⊢
2	instantiation	8, 4, 5	⊢
	: , : , :
3	instantiation	6, 36, 15, 27, 26, 11^, 7^	⊢
	: , : , : , :
4	instantiation	8, 9, 10	⊢
	: , : , :
5	instantiation	45, 11	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.division.prod_of_fracs
7	instantiation	17, 12, 13	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_right_side_into
9	instantiation	14, 36, 15, 27, 16, 26	⊢
	: , : , : , : , :
10	instantiation	17, 18, 19	⊢
	: , : , :
11	instantiation	40, 36	⊢
	:
12	instantiation	20, 74, 21, 22, 23, 24	⊢
	: , : , : , :
13	instantiation	25, 26, 27, 41, 28^, 29^, 30^*	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
15	instantiation	77, 64, 31	⊢
	: , : , :
16	instantiation	77, 38, 32	⊢
	: , : , :
17	axiom		⊢
	proveit.logic.equality.equals_transitivity
18	instantiation	45, 33	⊢
	: , : , :
19	instantiation	45, 34	⊢
	: , : , :
20	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
21	instantiation	35	⊢
	: , :
22	instantiation	35	⊢
	: , :
23	instantiation	55, 36	⊢
	:
24	instantiation	54, 41	⊢
	:
25	theorem		⊢
	proveit.numbers.division.frac_cancel_left
26	instantiation	77, 38, 37	⊢
	: , : , :
27	instantiation	77, 38, 39	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
29	instantiation	55, 41	⊢
	:
30	instantiation	40, 41	⊢
	:
31	instantiation	77, 71, 42	⊢
	: , : , :
32	instantiation	77, 49, 43	⊢
	: , : , :
33	instantiation	45, 44	⊢
	: , : , :
34	instantiation	45, 46	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	instantiation	77, 64, 47	⊢
	: , : , :
37	instantiation	77, 49, 48	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
39	instantiation	77, 49, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.division.frac_one_denom
41	instantiation	77, 64, 51	⊢
	: , : , :
42	instantiation	77, 75, 52	⊢
	: , : , :
43	instantiation	77, 59, 53	⊢
	: , : , :
44	instantiation	54, 56	⊢
	:
45	axiom		⊢
	proveit.logic.equality.substitution
46	instantiation	55, 56	⊢
	:
47	instantiation	77, 71, 57	⊢
	: , : , :
48	instantiation	77, 59, 58	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
50	instantiation	77, 59, 60	⊢
	: , : , :
51	instantiation	77, 71, 61	⊢
	: , : , :
52	instantiation	77, 78, 62	⊢
	: , : , :
53	instantiation	77, 68, 63	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
55	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
56	instantiation	77, 64, 65	⊢
	: , : , :
57	instantiation	77, 75, 66	⊢
	: , : , :
58	instantiation	77, 68, 67	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
60	instantiation	77, 68, 69	⊢
	: , : , :
61	instantiation	77, 75, 70	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
65	instantiation	77, 71, 72	⊢
	: , : , :
66	instantiation	77, 78, 73	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
70	instantiation	77, 78, 74	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
72	instantiation	77, 75, 76	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
74	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
76	instantiation	77, 78, 79	⊢
	: , : , :
77	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
78	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements