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	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
2	instantiation	8, 4, 5	⊢
	: , :
3	instantiation	6, 7	⊢
	: , :
4	instantiation	8, 9, 68	⊢
	: , :
5	instantiation	74, 10, 11	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
7	instantiation	12, 37, 13, 38, 14, 15^, 16^	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
9	instantiation	74, 17, 18	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
11	instantiation	19, 60	⊢
	:
12	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
14	instantiation	20, 61	⊢
	:
15	instantiation	40, 21, 22	⊢
	: , : , :
16	instantiation	23, 24, 25, 26	⊢
	: , : , : , :
17	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
18	instantiation	66, 27	⊢
	:
19	theorem		⊢
	proveit.numbers.negation.nat_pos_closure
20	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
21	instantiation	28, 29	⊢
	:
22	instantiation	49, 29, 30	⊢
	: , :
23	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
24	instantiation	47, 50, 31, 32, 33	⊢
	: , : , :
25	instantiation	34	⊢
	:
26	instantiation	35, 36	⊢
	: , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
28	theorem		⊢
	proveit.numbers.addition.elim_zero_right
29	instantiation	74, 64, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
31	instantiation	74, 64, 38	⊢
	: , : , :
32	instantiation	74, 64, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_3
34	axiom		⊢
	proveit.logic.equality.equals_reflexivity
35	theorem		⊢
	proveit.logic.equality.equals_reversal
36	instantiation	40, 41, 42	⊢
	: , : , :
37	instantiation	74, 43, 44	⊢
	: , : , :
38	instantiation	74, 69, 45	⊢
	: , : , :
39	instantiation	74, 69, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.equality.sub_right_side_into
41	instantiation	47, 50, 58, 48	⊢
	: , : , :
42	instantiation	49, 50, 51	⊢
	: , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
44	instantiation	74, 52, 53	⊢
	: , : , :
45	instantiation	74, 72, 54	⊢
	: , : , :
46	instantiation	74, 72, 55	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
48	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
49	theorem		⊢
	proveit.numbers.addition.commutation
50	instantiation	74, 64, 56	⊢
	: , : , :
51	instantiation	57, 58	⊢
	:
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
53	instantiation	74, 59, 60	⊢
	: , : , :
54	instantiation	74, 75, 61	⊢
	: , : , :
55	instantiation	74, 75, 62	⊢
	: , : , :
56	instantiation	74, 69, 63	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.negation.complex_closure
58	instantiation	74, 64, 65	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
60	instantiation	66, 67	⊢
	:
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
63	instantiation	74, 72, 68	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
65	instantiation	74, 69, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.negation.int_neg_closure
67	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
68	instantiation	74, 75, 71	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
70	instantiation	74, 72, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
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.nat2
^*equality replacement requirements