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	46	⊢
2	instantiation	4, 5, 73, 66, 6, 7, 8, 62, 9	⊢
	: , : , : , : , : , :
3	instantiation	54, 10	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.association
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	instantiation	11	⊢
	: , :
8	instantiation	12, 41, 62, 13	⊢
	: , :
9	instantiation	71, 64, 14	⊢
	: , : , :
10	instantiation	21, 15, 16	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12	theorem		⊢
	proveit.numbers.division.div_complex_closure
13	instantiation	17, 60	⊢
	:
14	instantiation	18, 19, 20	⊢
	: , : , :
15	instantiation	21, 22, 23	⊢
	: , : , :
16	instantiation	24, 25, 26, 27	⊢
	: , : , : , :
17	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
18	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
19	instantiation	28, 29	⊢
	: , :
20	assumption		⊢
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	30, 41, 31, 32	⊢
	: , : , : , : , :
23	instantiation	46, 33, 34	⊢
	: , : , :
24	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
25	instantiation	54, 35	⊢
	: , : , :
26	instantiation	54, 35	⊢
	: , : , :
27	instantiation	61, 41	⊢
	:
28	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
30	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
31	instantiation	71, 37, 36	⊢
	: , : , :
32	instantiation	71, 37, 38	⊢
	: , : , :
33	instantiation	54, 39	⊢
	: , : , :
34	instantiation	54, 40	⊢
	: , : , :
35	instantiation	56, 41	⊢
	:
36	instantiation	71, 43, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
38	instantiation	71, 43, 44	⊢
	: , : , :
39	instantiation	54, 45	⊢
	: , : , :
40	instantiation	46, 47, 48	⊢
	: , : , :
41	instantiation	71, 64, 49	⊢
	: , : , :
42	instantiation	71, 51, 50	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
44	instantiation	71, 51, 52	⊢
	: , : , :
45	instantiation	53, 62	⊢
	:
46	axiom		⊢
	proveit.logic.equality.equals_transitivity
47	instantiation	54, 55	⊢
	: , : , :
48	instantiation	56, 62	⊢
	:
49	instantiation	71, 67, 57	⊢
	: , : , :
50	instantiation	71, 59, 58	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
52	instantiation	71, 59, 60	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
54	axiom		⊢
	proveit.logic.equality.substitution
55	instantiation	61, 62	⊢
	:
56	theorem		⊢
	proveit.numbers.division.frac_one_denom
57	instantiation	71, 69, 63	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
61	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
62	instantiation	71, 64, 65	⊢
	: , : , :
63	instantiation	71, 72, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
65	instantiation	71, 67, 68	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
68	instantiation	71, 69, 70	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
70	instantiation	71, 72, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat2