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^, 7^	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	reference	28	⊢
3	instantiation	8, 33, 11	⊢
	: , :
4	instantiation	102, 95, 9	⊢
	: , : , :
5	instantiation	10, 33, 11, 53, 12, 13	⊢
	: , : , :
6	instantiation	47, 14, 15	⊢
	: , : , :
7	instantiation	47, 16, 17	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
9	instantiation	18, 46, 68	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
12	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
13	instantiation	19, 58	⊢
	:
14	instantiation	23, 20	⊢
	: , : , :
15	instantiation	21, 22	⊢
	:
16	instantiation	23, 24	⊢
	: , : , :
17	instantiation	25, 81, 100, 98, 26^*	⊢
	: , : , : , :
18	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
19	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
20	instantiation	27, 29	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.elim_zero_left
22	instantiation	102, 87, 28	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.substitution
24	instantiation	76, 29	⊢
	:
25	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
26	instantiation	47, 30, 31	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
28	instantiation	102, 95, 32	⊢
	: , : , :
29	instantiation	102, 87, 33	⊢
	: , : , :
30	instantiation	59, 60, 34, 35, 36, 37	⊢
	: , : , : , :
31	instantiation	38, 39, 40, 41, 42^, 43^	⊢
	: , : , :
32	instantiation	44, 68, 94, 45	⊢
	: , :
33	instantiation	102, 95, 46	⊢
	: , : , :
34	instantiation	73	⊢
	: , :
35	instantiation	73	⊢
	: , :
36	instantiation	47, 48, 49	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.mult_6_3
38	theorem		⊢
	proveit.numbers.division.frac_cancel_left
39	instantiation	102, 51, 50	⊢
	: , : , :
40	instantiation	102, 51, 52	⊢
	: , : , :
41	instantiation	102, 87, 53	⊢
	: , : , :
42	instantiation	76, 54	⊢
	:
43	theorem		⊢
	proveit.numbers.numerals.decimals.mult_9_2
44	theorem		⊢
	proveit.numbers.division.div_rational_closure
45	instantiation	55, 56	⊢
	:
46	instantiation	102, 57, 58	⊢
	: , : , :
47	axiom		⊢
	proveit.logic.equality.equals_transitivity
48	instantiation	59, 60, 61, 62, 63, 64	⊢
	: , : , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_6
50	instantiation	102, 66, 65	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
52	instantiation	102, 66, 67	⊢
	: , : , :
53	instantiation	102, 95, 68	⊢
	: , : , :
54	instantiation	102, 87, 69	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
58	instantiation	70, 71, 72	⊢
	: , :
59	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
61	instantiation	73	⊢
	: , :
62	instantiation	73	⊢
	: , :
63	instantiation	74, 75	⊢
	:
64	instantiation	76, 77	⊢
	:
65	instantiation	102, 79, 78	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
67	instantiation	102, 79, 80	⊢
	: , : , :
68	instantiation	102, 99, 81	⊢
	: , : , :
69	instantiation	102, 95, 82	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
71	instantiation	102, 84, 83	⊢
	: , : , :
72	instantiation	102, 84, 85	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
74	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
75	instantiation	102, 87, 86	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
77	instantiation	102, 87, 88	⊢
	: , : , :
78	instantiation	102, 90, 89	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
80	instantiation	102, 90, 91	⊢
	: , : , :
81	instantiation	102, 103, 92	⊢
	: , : , :
82	instantiation	102, 99, 93	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
85	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
86	instantiation	102, 95, 94	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
88	instantiation	102, 95, 96	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
90	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
91	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
92	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
93	instantiation	102, 103, 97	⊢
	: , : , :
94	instantiation	102, 99, 98	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
96	instantiation	102, 99, 100	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
98	instantiation	102, 103, 101	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
100	instantiation	102, 103, 104	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
102	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
103	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
104	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
^*equality replacement requirements