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