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	31	⊢
3	instantiation	8, 37, 11	⊢
	: , :
4	instantiation	94, 88, 9	⊢
	: , : , :
5	instantiation	10, 37, 11, 12, 13, 14	⊢
	: , : , :
6	instantiation	49, 15, 16	⊢
	: , : , :
7	instantiation	49, 17, 18	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
9	instantiation	19, 48, 20	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
12	instantiation	94, 88, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
14	instantiation	21, 57	⊢
	:
15	instantiation	25, 22	⊢
	: , : , :
16	instantiation	23, 24	⊢
	:
17	instantiation	25, 26	⊢
	: , : , :
18	instantiation	27, 29, 92, 90, 28^*	⊢
	: , : , : , :
19	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
20	instantiation	94, 91, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
22	instantiation	30, 32	⊢
	:
23	theorem		⊢
	proveit.numbers.addition.elim_zero_left
24	instantiation	94, 82, 31	⊢
	: , : , :
25	axiom		⊢
	proveit.logic.equality.substitution
26	instantiation	73, 32	⊢
	:
27	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
28	instantiation	49, 33, 34	⊢
	: , : , :
29	instantiation	94, 95, 35	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
31	instantiation	94, 88, 36	⊢
	: , : , :
32	instantiation	94, 82, 37	⊢
	: , : , :
33	instantiation	58, 93, 38, 39, 40, 41	⊢
	: , : , : , :
34	instantiation	42, 43, 44, 72, 45^, 46^	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
36	instantiation	94, 56, 47	⊢
	: , : , :
37	instantiation	94, 88, 48	⊢
	: , : , :
38	instantiation	70	⊢
	: , :
39	instantiation	70	⊢
	: , :
40	instantiation	49, 50, 51	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.mult_6_2
42	theorem		⊢
	proveit.numbers.division.frac_cancel_left
43	instantiation	94, 53, 52	⊢
	: , : , :
44	instantiation	94, 53, 54	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
46	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_3
47	instantiation	67, 68, 55	⊢
	: , :
48	instantiation	94, 56, 57	⊢
	: , : , :
49	axiom		⊢
	proveit.logic.equality.equals_transitivity
50	instantiation	58, 93, 59, 60, 61, 62	⊢
	: , : , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_6
52	instantiation	94, 64, 63	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
54	instantiation	94, 64, 65	⊢
	: , : , :
55	instantiation	94, 79, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
57	instantiation	67, 68, 69	⊢
	: , :
58	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
59	instantiation	70	⊢
	: , :
60	instantiation	70	⊢
	: , :
61	instantiation	71, 72	⊢
	:
62	instantiation	73, 74	⊢
	:
63	instantiation	94, 76, 75	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
65	instantiation	94, 76, 77	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
67	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
68	instantiation	94, 79, 78	⊢
	: , : , :
69	instantiation	94, 79, 80	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
71	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
72	instantiation	94, 82, 81	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
74	instantiation	94, 82, 83	⊢
	: , : , :
75	instantiation	94, 85, 84	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
77	instantiation	94, 85, 86	⊢
	: , : , :
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.posnat6
81	instantiation	94, 88, 87	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
83	instantiation	94, 88, 89	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
85	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
86	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
87	instantiation	94, 91, 90	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
89	instantiation	94, 91, 92	⊢
	: , : , :
90	instantiation	94, 95, 93	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
92	instantiation	94, 95, 96	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
94	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
95	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
96	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
^*equality replacement requirements