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