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