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	63	⊢
3	instantiation	85, 67, 7	⊢
	: , : , :
4	instantiation	8, 63, 17	⊢
	: , :
5	instantiation	9, 58, 10, 11, 12, 13^*	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
7	instantiation	42, 14, 68	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
9	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
10	instantiation	85, 81, 15	⊢
	: , : , :
11	instantiation	85, 16, 17	⊢
	: , : , :
12	instantiation	18, 19, 57, 63, 20	⊢
	: , : , :
13	instantiation	21, 72, 84, 22^, 23^, 24^*	⊢
	: , : , : , :
14	instantiation	85, 73, 25	⊢
	: , : , :
15	instantiation	85, 26, 27	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
17	instantiation	28, 29, 57, 30	⊢
	: , :
18	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
19	instantiation	85, 31, 32	⊢
	: , : , :
20	instantiation	33, 58, 70, 78, 34, 35, 36^*	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
22	instantiation	37, 49	⊢
	:
23	instantiation	38, 39, 40	⊢
	: , : , :
24	instantiation	41, 49	⊢
	:
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
26	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
27	instantiation	42, 43, 68	⊢
	: , :
28	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
29	instantiation	85, 67, 43	⊢
	: , : , :
30	instantiation	44, 45	⊢
	:
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
32	instantiation	85, 46, 87	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
34	instantiation	47, 77, 78, 79	⊢
	: , : , :
35	instantiation	48, 80	⊢
	:
36	instantiation	60, 49	⊢
	:
37	theorem		⊢
	proveit.numbers.division.frac_one_denom
38	axiom		⊢
	proveit.logic.equality.equals_transitivity
39	instantiation	50, 80, 51, 52, 53, 54	⊢
	: , : , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
41	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
42	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
43	instantiation	85, 73, 55	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
45	instantiation	85, 56, 57	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
48	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
49	instantiation	85, 66, 58	⊢
	: , : , :
50	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
51	instantiation	59	⊢
	: , :
52	instantiation	59	⊢
	: , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
54	instantiation	60, 61	⊢
	:
55	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
57	instantiation	62, 63, 64	⊢
	: , :
58	instantiation	85, 81, 65	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
60	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
61	instantiation	85, 66, 78	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
63	instantiation	85, 67, 68	⊢
	: , : , :
64	instantiation	69, 70, 71	⊢
	:
65	instantiation	85, 83, 72	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
68	instantiation	85, 73, 74	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
70	instantiation	75, 77, 78, 79	⊢
	: , : , :
71	instantiation	76, 77, 78, 79	⊢
	: , : , :
72	instantiation	85, 86, 80	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
74	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
78	instantiation	85, 81, 82	⊢
	: , : , :
79	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
82	instantiation	85, 83, 84	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
84	instantiation	85, 86, 87	⊢
	: , : , :
85	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
86	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements