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, 13^*	, , ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.association
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	reference	75	⊢
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	instantiation	43	⊢
	: , :
7	instantiation	14	⊢
	: , : , :
8	reference	44	⊢
9	instantiation	15, 21, 51, 16	⊢
	: , :
10	assumption		⊢
11	assumption		⊢
12	instantiation	17, 18, 19	⊢
	: , :
13	instantiation	20, 44, 21, 38, 37, 22^, 23^	⊢
	: , : , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
15	theorem		⊢
	proveit.numbers.division.div_complex_closure
16	instantiation	24, 67	⊢
	:
17	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
18	assumption		⊢
19	instantiation	73, 57, 25	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.division.prod_of_fracs
21	instantiation	73, 57, 30	⊢
	: , : , :
22	instantiation	50, 44	⊢
	:
23	instantiation	26, 27, 28	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
25	instantiation	29, 30	⊢
	:
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	31, 75, 32, 33, 34, 35	⊢
	: , : , : , :
28	instantiation	36, 37, 38, 51, 39^, 40^, 41^*	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.negation.real_closure
30	instantiation	73, 64, 42	⊢
	: , : , :
31	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
32	instantiation	43	⊢
	: , :
33	instantiation	43	⊢
	: , :
34	instantiation	49, 44	⊢
	:
35	instantiation	45, 51	⊢
	:
36	theorem		⊢
	proveit.numbers.division.frac_cancel_left
37	instantiation	73, 47, 46	⊢
	: , : , :
38	instantiation	73, 47, 48	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
40	instantiation	49, 51	⊢
	:
41	instantiation	50, 51	⊢
	:
42	instantiation	73, 70, 52	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44	instantiation	73, 57, 53	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
46	instantiation	73, 55, 54	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
48	instantiation	73, 55, 56	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
50	theorem		⊢
	proveit.numbers.division.frac_one_denom
51	instantiation	73, 57, 58	⊢
	: , : , :
52	instantiation	73, 74, 59	⊢
	: , : , :
53	instantiation	73, 64, 60	⊢
	: , : , :
54	instantiation	73, 62, 61	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
56	instantiation	73, 62, 63	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
58	instantiation	73, 64, 65	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
60	instantiation	73, 70, 66	⊢
	: , : , :
61	instantiation	73, 68, 67	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
63	instantiation	73, 68, 69	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
65	instantiation	73, 70, 71	⊢
	: , : , :
66	instantiation	73, 74, 72	⊢
	: , : , :
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	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
71	instantiation	73, 74, 75	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
73	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements