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