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