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	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5, 6, 7, 8, 9	⊢
	: , : , : , :
3	instantiation	10, 11, 22, 12, 13	⊢
	: , : , :
4	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
6	instantiation	14	⊢
	: , :
7	instantiation	14	⊢
	: , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.mult_5_3
9	instantiation	15, 22, 16, 17^*	⊢
	: , :
10	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
11	instantiation	74, 68, 18	⊢
	: , : , :
12	instantiation	74, 68, 19	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.add_9_6
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
16	instantiation	74, 68, 20	⊢
	: , : , :
17	instantiation	21, 22	⊢
	:
18	instantiation	74, 70, 23	⊢
	: , : , :
19	instantiation	74, 70, 24	⊢
	: , : , :
20	instantiation	74, 70, 25	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
22	instantiation	74, 68, 26	⊢
	: , : , :
23	instantiation	74, 72, 27	⊢
	: , : , :
24	instantiation	74, 72, 28	⊢
	: , : , :
25	instantiation	74, 72, 29	⊢
	: , : , :
26	instantiation	74, 70, 30	⊢
	: , : , :
27	instantiation	74, 75, 31	⊢
	: , : , :
28	instantiation	74, 32, 33	⊢
	: , : , :
29	instantiation	74, 75, 48	⊢
	: , : , :
30	instantiation	74, 72, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
32	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
33	instantiation	35, 48, 36, 37, 38	⊢
	: , : , :
34	instantiation	74, 75, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
36	instantiation	41, 48, 40	⊢
	:
37	instantiation	41, 76, 42	⊢
	:
38	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
40	instantiation	45, 43, 44	⊢
	: , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.n_in_digits
42	instantiation	45, 46, 47	⊢
	: , :
43	instantiation	58, 48	⊢
	:
44	instantiation	49, 50	⊢
	:
45	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
46	instantiation	58, 76	⊢
	:
47	instantiation	51, 69, 52, 53, 54, 55^, 56^	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
51	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
53	instantiation	74, 70, 57	⊢
	: , : , :
54	instantiation	58, 67	⊢
	:
55	instantiation	59, 60, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_5
57	instantiation	74, 72, 62	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
59	theorem		⊢
	proveit.logic.equality.sub_right_side_into
60	instantiation	63, 65	⊢
	:
61	instantiation	64, 65, 66	⊢
	: , :
62	instantiation	74, 75, 67	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.addition.elim_zero_right
64	theorem		⊢
	proveit.numbers.addition.commutation
65	instantiation	74, 68, 69	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
68	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
69	instantiation	74, 70, 71	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
71	instantiation	74, 72, 73	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
73	instantiation	74, 75, 76	⊢
	: , : , :
74	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
^*equality replacement requirements