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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	5, 7, 6, 75, 10, 8, 11, 21, 12, 4	⊢
	: , : , : , : , : , :
3	instantiation	5, 6, 51, 7, 8, 9, 10, 11, 21, 12, 14, 15	⊢
	: , : , : , : , : , :
4	instantiation	13, 14, 15	⊢
	: , :
5	theorem		⊢
	proveit.numbers.multiplication.disassociation
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	instantiation	16	⊢
	: , : , :
9	instantiation	17	⊢
	: , :
10	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
11	instantiation	76, 31, 28	⊢
	: , : , :
12	instantiation	76, 31, 18	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
14	instantiation	76, 31, 19	⊢
	: , : , :
15	instantiation	20, 21, 22	⊢
	: , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	instantiation	23, 24, 25	⊢
	: , :
19	instantiation	26, 27, 28, 29	⊢
	: , :
20	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
21	instantiation	76, 31, 30	⊢
	: , : , :
22	instantiation	76, 31, 32	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
24	instantiation	33, 34	⊢
	:
25	instantiation	35, 36	⊢
	:
26	theorem		⊢
	proveit.numbers.division.div_real_closure
27	instantiation	76, 49, 37	⊢
	: , : , :
28	instantiation	76, 49, 38	⊢
	: , : , :
29	instantiation	39, 70	⊢
	:
30	instantiation	76, 40, 41	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	76, 49, 42	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.negation.real_closure
34	instantiation	43, 44, 45	⊢
	: , :
35	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
36	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
37	instantiation	76, 52, 68	⊢
	: , : , :
38	instantiation	76, 52, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
42	instantiation	76, 52, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
44	instantiation	76, 49, 48	⊢
	: , : , :
45	instantiation	76, 49, 50	⊢
	: , : , :
46	instantiation	76, 74, 51	⊢
	: , : , :
47	instantiation	72, 68	⊢
	:
48	instantiation	76, 52, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	76, 54, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	instantiation	76, 56, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
55	instantiation	58, 59, 60	⊢
	: , :
56	instantiation	61, 62, 73	⊢
	: , :
57	assumption		⊢
58	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
59	instantiation	76, 63, 64	⊢
	: , : , :
60	instantiation	72, 65	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
62	instantiation	66, 67, 68	⊢
	: , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
64	instantiation	76, 69, 70	⊢
	: , : , :
65	instantiation	76, 77, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
67	instantiation	72, 73	⊢
	:
68	instantiation	76, 74, 75	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
71	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
72	theorem		⊢
	proveit.numbers.negation.int_closure
73	instantiation	76, 77, 78	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
78	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos