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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less_eq
2	reference	62	⊢
3	instantiation	28, 7, 62, 16	⊢
	: , :
4	instantiation	8, 62, 18	⊢
	: , :
5	instantiation	9, 57, 10, 11, 12, 13^*	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
7	instantiation	84, 66, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
9	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
10	instantiation	15, 77, 57, 16	⊢
	: , :
11	instantiation	84, 17, 18	⊢
	: , : , :
12	instantiation	19, 20, 56, 62, 21	⊢
	: , : , :
13	instantiation	22, 71, 83, 23^, 24^, 25^*	⊢
	: , : , : , :
14	instantiation	84, 72, 26	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.division.div_real_closure
16	instantiation	27, 73	⊢
	:
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
18	instantiation	28, 29, 56, 30	⊢
	: , :
19	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
20	instantiation	84, 31, 32	⊢
	: , : , :
21	instantiation	33, 57, 69, 77, 34, 35, 36^*	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
23	instantiation	37, 48	⊢
	:
24	instantiation	38, 39, 40	⊢
	: , : , :
25	instantiation	41, 48	⊢
	:
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
29	instantiation	84, 66, 42	⊢
	: , : , :
30	instantiation	43, 44	⊢
	:
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
32	instantiation	84, 45, 86	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
34	instantiation	46, 76, 77, 78	⊢
	: , : , :
35	instantiation	47, 79	⊢
	:
36	instantiation	59, 48	⊢
	:
37	theorem		⊢
	proveit.numbers.division.frac_one_denom
38	axiom		⊢
	proveit.logic.equality.equals_transitivity
39	instantiation	49, 79, 50, 51, 52, 53	⊢
	: , : , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
41	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
42	instantiation	84, 72, 54	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
44	instantiation	84, 55, 56	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
48	instantiation	84, 65, 57	⊢
	: , : , :
49	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
50	instantiation	58	⊢
	: , :
51	instantiation	58	⊢
	: , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
53	instantiation	59, 60	⊢
	:
54	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
56	instantiation	61, 62, 63	⊢
	: , :
57	instantiation	84, 80, 64	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
59	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
60	instantiation	84, 65, 77	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
62	instantiation	84, 66, 67	⊢
	: , : , :
63	instantiation	68, 69, 70	⊢
	:
64	instantiation	84, 82, 71	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
67	instantiation	84, 72, 73	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
69	instantiation	74, 76, 77, 78	⊢
	: , : , :
70	instantiation	75, 76, 77, 78	⊢
	: , : , :
71	instantiation	84, 85, 79	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
73	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
77	instantiation	84, 80, 81	⊢
	: , : , :
78	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
81	instantiation	84, 82, 83	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
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.nat1
^*equality replacement requirements