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	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.disassociation
2	reference	76	⊢
3	reference	86	⊢
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	10	⊢
	: , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	instantiation	84, 13, 11	⊢
	: , : , :
8	instantiation	84, 13, 12	⊢
	: , : , :
9	instantiation	84, 13, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11	instantiation	84, 38, 15	⊢
	: , : , :
12	instantiation	84, 38, 16	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
14	modus ponens	17, 18	⊢
15	instantiation	84, 19, 20	⊢
	: , : , :
16	instantiation	84, 43, 83	⊢
	: , : , :
17	instantiation	21	⊢
	: , : , :
18	generalization	22	⊢
19	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
20	instantiation	23, 24, 25	⊢
	: , :
21	theorem		⊢
	proveit.numbers.summation.summation_real_closure
22	instantiation	26, 27, 28, 29	, ⊢
	: , :
23	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
24	instantiation	84, 30, 70	⊢
	: , : , :
25	instantiation	84, 30, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.division.div_real_closure
27	instantiation	84, 38, 32	⊢
	: , : , :
28	instantiation	33, 34, 86	, ⊢
	: , :
29	instantiation	35, 36, 37	, ⊢
	: , :
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
32	instantiation	84, 43, 73	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
34	instantiation	84, 38, 39	, ⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
36	instantiation	84, 41, 40	, ⊢
	: , : , :
37	instantiation	84, 41, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
39	instantiation	84, 43, 47	, ⊢
	: , : , :
40	instantiation	84, 45, 44	, ⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
42	instantiation	84, 45, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	instantiation	60, 47, 48	, ⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
47	instantiation	84, 49, 56	, ⊢
	: , : , :
48	instantiation	66, 50, 51	, ⊢
	: , : , :
49	instantiation	71, 54, 55	⊢
	: , :
50	instantiation	52, 53	⊢
	:
51	instantiation	72, 54, 55, 56	, ⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
53	instantiation	57, 58, 70	⊢
	: , :
54	instantiation	77, 61, 73	⊢
	: , :
55	instantiation	77, 78, 59	⊢
	: , :
56	assumption		⊢
57	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
58	instantiation	60, 61, 62	⊢
	:
59	instantiation	84, 63, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
61	instantiation	84, 65, 75	⊢
	: , : , :
62	instantiation	66, 67, 68	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
64	instantiation	69, 70	⊢
	:
65	instantiation	71, 73, 74	⊢
	: , :
66	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
67	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
68	instantiation	72, 73, 74, 75	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.negation.int_neg_closure
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
71	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
72	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
73	instantiation	84, 85, 76	⊢
	: , : , :
74	instantiation	77, 78, 79	⊢
	: , :
75	assumption		⊢
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
77	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
78	instantiation	84, 80, 81	⊢
	: , : , :
79	instantiation	82, 83	⊢
	:
80	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
81	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
82	theorem		⊢
	proveit.numbers.negation.int_closure
83	instantiation	84, 85, 86	⊢
	: , : , :
84	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
85	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
86	theorem		⊢
	proveit.numbers.numerals.decimals.nat2