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^*	⊢
	: , :
1	theorem		⊢
	proveit.numbers.rounding.ceil_of_real_above_int
2	reference	85	⊢
3	instantiation	6, 24, 9, 7	⊢
	: , :
4	instantiation	8, 24, 9, 10, 26, 11^*	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
6	theorem		⊢
	proveit.numbers.logarithms.log_real_pos_real_closure
7	instantiation	12, 13	⊢
	: , :
8	theorem		⊢
	proveit.numbers.logarithms.log_increasing_less
9	instantiation	14, 15, 24, 16	⊢
	: , :
10	instantiation	17, 64, 18, 19, 20, 21^, 22^	⊢
	: , : , :
11	instantiation	23, 24	⊢
	:
12	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
13	instantiation	25, 88, 80, 26	⊢
	: , :
14	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
15	instantiation	86, 39, 27	⊢
	: , : , :
16	instantiation	28, 83	⊢
	:
17	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
18	instantiation	29, 58, 32	⊢
	: , :
19	instantiation	86, 78, 30	⊢
	: , : , :
20	instantiation	31, 58, 32, 73, 33, 34	⊢
	: , : , :
21	instantiation	54, 35, 36	⊢
	: , : , :
22	instantiation	54, 37, 38	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.logarithms.log_eq_1
24	instantiation	86, 39, 77	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
26	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
27	instantiation	86, 82, 40	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
29	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
30	instantiation	41, 65, 79	⊢
	: , :
31	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
33	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
34	instantiation	42, 71	⊢
	:
35	instantiation	45, 43	⊢
	: , : , :
36	instantiation	44, 57	⊢
	:
37	instantiation	45, 46	⊢
	: , : , :
38	instantiation	47, 85, 74, 48^, 49^, 50^*	⊢
	: , : , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
41	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
43	instantiation	51, 52	⊢
	:
44	theorem		⊢
	proveit.numbers.addition.elim_zero_left
45	axiom		⊢
	proveit.logic.equality.substitution
46	instantiation	67, 52	⊢
	:
47	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
48	instantiation	53, 57	⊢
	:
49	instantiation	54, 55, 56	⊢
	: , : , :
50	instantiation	67, 57	⊢
	:
51	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
52	instantiation	86, 72, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.division.frac_one_denom
54	axiom		⊢
	proveit.logic.equality.equals_transitivity
55	instantiation	59, 80, 60, 61, 62, 63	⊢
	: , : , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_4
57	instantiation	86, 72, 64	⊢
	: , : , :
58	instantiation	86, 78, 65	⊢
	: , : , :
59	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
60	instantiation	66	⊢
	: , :
61	instantiation	66	⊢
	: , :
62	instantiation	67, 68	⊢
	:
63	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
64	instantiation	86, 78, 69	⊢
	: , : , :
65	instantiation	86, 70, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
67	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
68	instantiation	86, 72, 73	⊢
	: , : , :
69	instantiation	86, 84, 74	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
71	instantiation	75, 76, 77	⊢
	: , :
72	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
73	instantiation	86, 78, 79	⊢
	: , : , :
74	instantiation	86, 87, 80	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
76	instantiation	86, 82, 81	⊢
	: , : , :
77	instantiation	86, 82, 83	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
79	instantiation	86, 84, 85	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
81	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
83	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
85	instantiation	86, 87, 88	⊢
	: , : , :
86	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements