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	4, 5, 39, 70, 6, 7, 14, 10, 8	⊢
	: , : , : , : , : , :
3	instantiation	9, 14, 10, 11	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	instantiation	12	⊢
	: , :
8	instantiation	13, 14	⊢
	:
9	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
10	instantiation	68, 17, 15	⊢
	: , : , :
11	instantiation	16	⊢
	:
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	theorem		⊢
	proveit.numbers.negation.complex_closure
14	instantiation	68, 17, 18	⊢
	: , : , :
15	instantiation	68, 64, 19	⊢
	: , : , :
16	axiom		⊢
	proveit.logic.equality.equals_reflexivity
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
18	instantiation	20, 21, 22	⊢
	: , : , :
19	instantiation	68, 66, 23	⊢
	: , : , :
20	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
21	instantiation	24, 25	⊢
	: , :
22	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
23	instantiation	26, 27	⊢
	:
24	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
26	axiom		⊢
	proveit.numbers.rounding.ceil_is_an_int
27	instantiation	28, 43, 29, 30	⊢
	: , :
28	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
29	instantiation	31, 43, 32	⊢
	: , :
30	instantiation	33, 34	⊢
	: , :
31	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
32	instantiation	35, 36, 37	⊢
	: , :
33	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
34	instantiation	38, 70, 39, 40	⊢
	: , :
35	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
36	instantiation	41, 42, 43, 44	⊢
	: , :
37	instantiation	45, 46, 47	⊢
	: , :
38	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
40	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
41	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
42	instantiation	68, 49, 48	⊢
	: , : , :
43	instantiation	68, 49, 50	⊢
	: , : , :
44	instantiation	51, 58	⊢
	:
45	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
46	instantiation	52, 53, 54	⊢
	:
47	instantiation	55, 62	⊢
	:
48	instantiation	68, 57, 56	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
50	instantiation	68, 57, 58	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
53	instantiation	59, 61, 62, 63	⊢
	: , : , :
54	instantiation	60, 61, 62, 63	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.negation.real_closure
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
58	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
62	instantiation	68, 64, 65	⊢
	: , : , :
63	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
65	instantiation	68, 66, 67	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
67	instantiation	68, 69, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat1