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	24	⊢
2	instantiation	52, 4	⊢
	: , : , :
3	instantiation	24, 5, 6	⊢
	: , : , :
4	instantiation	7, 33, 23, 76, 8^, 9^	⊢
	: , : , :
5	instantiation	15, 10, 11	⊢
	: , : , :
6	instantiation	12, 43, 22, 34, 33, 18^, 13^	⊢
	: , : , : , :
7	theorem		⊢
	proveit.numbers.exponentiation.neg_power_of_quotient
8	instantiation	14, 63	⊢
	:
9	instantiation	14, 48	⊢
	:
10	instantiation	15, 16, 17	⊢
	: , : , :
11	instantiation	52, 18	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.division.prod_of_fracs
13	instantiation	24, 19, 20	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
15	theorem		⊢
	proveit.logic.equality.sub_right_side_into
16	instantiation	21, 43, 22, 34, 23, 33	⊢
	: , : , : , : , :
17	instantiation	24, 25, 26	⊢
	: , : , :
18	instantiation	47, 43	⊢
	:
19	instantiation	27, 81, 28, 29, 30, 31	⊢
	: , : , : , :
20	instantiation	32, 33, 34, 48, 35^, 36^, 37^*	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
22	instantiation	84, 71, 38	⊢
	: , : , :
23	instantiation	84, 45, 39	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	52, 40	⊢
	: , : , :
26	instantiation	52, 41	⊢
	: , : , :
27	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
28	instantiation	42	⊢
	: , :
29	instantiation	42	⊢
	: , :
30	instantiation	62, 43	⊢
	:
31	instantiation	61, 48	⊢
	:
32	theorem		⊢
	proveit.numbers.division.frac_cancel_left
33	instantiation	84, 45, 44	⊢
	: , : , :
34	instantiation	84, 45, 46	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
36	instantiation	62, 48	⊢
	:
37	instantiation	47, 48	⊢
	:
38	instantiation	84, 78, 49	⊢
	: , : , :
39	instantiation	84, 56, 50	⊢
	: , : , :
40	instantiation	52, 51	⊢
	: , : , :
41	instantiation	52, 53	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	instantiation	84, 71, 54	⊢
	: , : , :
44	instantiation	84, 56, 55	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
46	instantiation	84, 56, 57	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.division.frac_one_denom
48	instantiation	84, 71, 58	⊢
	: , : , :
49	instantiation	84, 82, 59	⊢
	: , : , :
50	instantiation	84, 66, 60	⊢
	: , : , :
51	instantiation	61, 63	⊢
	:
52	axiom		⊢
	proveit.logic.equality.substitution
53	instantiation	62, 63	⊢
	:
54	instantiation	84, 78, 64	⊢
	: , : , :
55	instantiation	84, 66, 65	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
57	instantiation	84, 66, 67	⊢
	: , : , :
58	instantiation	84, 78, 68	⊢
	: , : , :
59	instantiation	84, 85, 69	⊢
	: , : , :
60	instantiation	84, 75, 70	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
62	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
63	instantiation	84, 71, 72	⊢
	: , : , :
64	instantiation	84, 82, 73	⊢
	: , : , :
65	instantiation	84, 75, 74	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
67	instantiation	84, 75, 76	⊢
	: , : , :
68	instantiation	84, 82, 77	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
72	instantiation	84, 78, 79	⊢
	: , : , :
73	instantiation	84, 85, 80	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
77	instantiation	84, 85, 81	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
79	instantiation	84, 82, 83	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
81	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
83	instantiation	84, 85, 86	⊢
	: , : , :
84	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
85	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
86	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements