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	50	⊢
2	instantiation	4, 71, 78, 5, 6, 7, 8, 67, 9	⊢
	: , : , : , : , : , :
3	instantiation	58, 10	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.association
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	instantiation	11	⊢
	: , :
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	76, 69, 12	⊢
	: , : , :
9	instantiation	76, 69, 13	⊢
	: , : , :
10	instantiation	20, 14, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12	instantiation	16, 17, 18	⊢
	: , : , :
13	instantiation	76, 72, 19	⊢
	: , : , :
14	instantiation	20, 21, 22	⊢
	: , : , :
15	instantiation	23, 24, 25, 26	⊢
	: , : , : , :
16	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
17	instantiation	27, 28	⊢
	: , :
18	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
19	instantiation	76, 29, 30	⊢
	: , : , :
20	theorem		⊢
	proveit.logic.equality.sub_right_side_into
21	instantiation	31, 45, 32, 33	⊢
	: , : , : , : , :
22	instantiation	50, 34, 35	⊢
	: , : , :
23	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
24	instantiation	58, 36	⊢
	: , : , :
25	instantiation	58, 36	⊢
	: , : , :
26	instantiation	61, 45	⊢
	:
27	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
29	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
30	instantiation	37, 38, 39	⊢
	: , :
31	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
32	instantiation	76, 41, 40	⊢
	: , : , :
33	instantiation	76, 41, 42	⊢
	: , : , :
34	instantiation	58, 43	⊢
	: , : , :
35	instantiation	58, 44	⊢
	: , : , :
36	instantiation	60, 45	⊢
	:
37	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
38	instantiation	76, 46, 65	⊢
	: , : , :
39	instantiation	76, 46, 63	⊢
	: , : , :
40	instantiation	76, 48, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
42	instantiation	76, 48, 49	⊢
	: , : , :
43	instantiation	50, 51, 52	⊢
	: , : , :
44	instantiation	58, 53	⊢
	: , : , :
45	instantiation	76, 69, 54	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
47	instantiation	76, 56, 55	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
49	instantiation	76, 56, 57	⊢
	: , : , :
50	axiom		⊢
	proveit.logic.equality.equals_transitivity
51	instantiation	58, 59	⊢
	: , : , :
52	instantiation	60, 67	⊢
	:
53	instantiation	61, 67	⊢
	:
54	instantiation	76, 72, 62	⊢
	: , : , :
55	instantiation	76, 64, 63	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
57	instantiation	76, 64, 65	⊢
	: , : , :
58	axiom		⊢
	proveit.logic.equality.substitution
59	instantiation	66, 67	⊢
	:
60	theorem		⊢
	proveit.numbers.division.frac_one_denom
61	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
62	instantiation	76, 74, 68	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
66	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
67	instantiation	76, 69, 70	⊢
	: , : , :
68	instantiation	76, 77, 71	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
70	instantiation	76, 72, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
73	instantiation	76, 74, 75	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
75	instantiation	76, 77, 78	⊢
	: , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat2