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	47	⊢
2	instantiation	47, 4, 5	⊢
	: , : , :
3	instantiation	63, 11	⊢
	:
4	instantiation	6, 7, 75, 68, 8, 9, 64, 10, 11	⊢
	: , : , : , : , : , :
5	instantiation	55, 12	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.multiplication.association
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	13	⊢
	: , :
10	instantiation	14, 43, 64, 15	⊢
	: , :
11	instantiation	73, 66, 16	⊢
	: , : , :
12	instantiation	23, 17, 18	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	theorem		⊢
	proveit.numbers.division.div_complex_closure
15	instantiation	19, 60	⊢
	:
16	instantiation	20, 21, 22	⊢
	: , : , :
17	instantiation	23, 24, 25	⊢
	: , : , :
18	instantiation	26, 27, 28, 29	⊢
	: , : , : , :
19	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
20	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
21	instantiation	30, 31	⊢
	: , :
22	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
23	theorem		⊢
	proveit.logic.equality.sub_right_side_into
24	instantiation	32, 43, 33, 34	⊢
	: , : , : , : , :
25	instantiation	47, 35, 36	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
27	instantiation	55, 37	⊢
	: , : , :
28	instantiation	55, 37	⊢
	: , : , :
29	instantiation	58, 43	⊢
	:
30	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
32	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
33	instantiation	73, 39, 38	⊢
	: , : , :
34	instantiation	73, 39, 40	⊢
	: , : , :
35	instantiation	55, 41	⊢
	: , : , :
36	instantiation	55, 42	⊢
	: , : , :
37	instantiation	57, 43	⊢
	:
38	instantiation	73, 45, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
40	instantiation	73, 45, 46	⊢
	: , : , :
41	instantiation	47, 48, 49	⊢
	: , : , :
42	instantiation	55, 50	⊢
	: , : , :
43	instantiation	73, 66, 51	⊢
	: , : , :
44	instantiation	73, 53, 52	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
46	instantiation	73, 53, 54	⊢
	: , : , :
47	axiom		⊢
	proveit.logic.equality.equals_transitivity
48	instantiation	55, 56	⊢
	: , : , :
49	instantiation	57, 64	⊢
	:
50	instantiation	58, 64	⊢
	:
51	instantiation	73, 69, 59	⊢
	: , : , :
52	instantiation	73, 61, 60	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
54	instantiation	73, 61, 62	⊢
	: , : , :
55	axiom		⊢
	proveit.logic.equality.substitution
56	instantiation	63, 64	⊢
	:
57	theorem		⊢
	proveit.numbers.division.frac_one_denom
58	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
59	instantiation	73, 71, 65	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
62	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
63	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
64	instantiation	73, 66, 67	⊢
	: , : , :
65	instantiation	73, 74, 68	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
67	instantiation	73, 69, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
70	instantiation	73, 71, 72	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	instantiation	73, 74, 75	⊢
	: , : , :
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