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^*	⊢
	: , :
1	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left_double
2	instantiation	7, 11, 5, 6	⊢
	: , :
3	instantiation	7, 12, 8, 9	⊢
	: , :
4	instantiation	10, 11, 12, 31, 32, 13^*	⊢
	: , : , : , :
5	instantiation	63, 44, 14	⊢
	: , : , :
6	instantiation	16, 60	⊢
	:
7	theorem		⊢
	proveit.numbers.division.div_complex_closure
8	instantiation	63, 44, 15	⊢
	: , : , :
9	instantiation	16, 62	⊢
	:
10	theorem		⊢
	proveit.numbers.division.prod_of_fracs
11	instantiation	63, 44, 17	⊢
	: , : , :
12	instantiation	63, 44, 18	⊢
	: , : , :
13	instantiation	19, 20, 21	⊢
	: , : , :
14	instantiation	63, 53, 22	⊢
	: , : , :
15	instantiation	63, 53, 23	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
17	instantiation	63, 53, 24	⊢
	: , : , :
18	instantiation	63, 53, 25	⊢
	: , : , :
19	axiom		⊢
	proveit.logic.equality.equals_transitivity
20	instantiation	26, 48, 27, 28, 29, 35	⊢
	: , : , : , :
21	instantiation	30, 31, 32, 33, 34^, 35^	⊢
	: , : , :
22	instantiation	63, 58, 36	⊢
	: , : , :
23	instantiation	63, 58, 37	⊢
	: , : , :
24	instantiation	63, 58, 38	⊢
	: , : , :
25	instantiation	63, 58, 39	⊢
	: , : , :
26	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
27	instantiation	40	⊢
	: , :
28	instantiation	40	⊢
	: , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_6
30	theorem		⊢
	proveit.numbers.division.frac_cancel_left
31	instantiation	63, 42, 41	⊢
	: , : , :
32	instantiation	63, 42, 43	⊢
	: , : , :
33	instantiation	63, 44, 45	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_4
35	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_5
36	instantiation	63, 64, 46	⊢
	: , : , :
37	instantiation	63, 64, 47	⊢
	: , : , :
38	instantiation	63, 64, 48	⊢
	: , : , :
39	instantiation	63, 64, 49	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
41	instantiation	63, 51, 50	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
43	instantiation	63, 51, 52	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	63, 53, 54	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
50	instantiation	63, 56, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
52	instantiation	63, 56, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
54	instantiation	63, 58, 59	⊢
	: , : , :
55	instantiation	63, 61, 60	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
57	instantiation	63, 61, 62	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
59	instantiation	63, 64, 65	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
62	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements