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.logic.equality.sub_right_side_into
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.core_expr_types.tuples.range_len
5	instantiation	71, 9, 10	⊢
	: , : , :
6	axiom		⊢
	proveit.logic.equality.equals_transitivity
7	instantiation	11, 52	⊢
	: , : , :
8	instantiation	12, 13, 14, 15	⊢
	: , : , : , :
9	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
10	instantiation	16, 27, 22, 17, 23, 18, 19, 73, 20	⊢
	: , : , : , : , :
11	axiom		⊢
	proveit.logic.equality.substitution
12	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
13	instantiation	21, 22, 27, 23, 28, 24, 32, 29, 25, 31	⊢
	: , : , : , : , : , :
14	instantiation	26, 27, 73, 28, 32, 29, 31	⊢
	: , : , : , :
15	instantiation	30, 31, 32, 33	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
17	instantiation	39	⊢
	: , :
18	instantiation	34, 35, 36	⊢
	:
19	instantiation	57, 37, 38	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
21	theorem		⊢
	proveit.numbers.addition.disassociation
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24	instantiation	39	⊢
	: , :
25	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
26	theorem		⊢
	proveit.numbers.addition.elim_zero_any
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
28	instantiation	39	⊢
	: , :
29	instantiation	71, 42, 40	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
31	instantiation	71, 42, 41	⊢
	: , : , :
32	instantiation	71, 42, 43	⊢
	: , : , :
33	instantiation	44	⊢
	:
34	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
35	instantiation	45, 46, 47	⊢
	: , :
36	instantiation	48, 49	⊢
	: , :
37	instantiation	67, 50	⊢
	: , :
38	instantiation	51, 52	⊢
	: , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	instantiation	71, 53, 54	⊢
	: , : , :
41	instantiation	71, 55, 56	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
43	instantiation	57, 58, 62	⊢
	: , : , :
44	axiom		⊢
	proveit.logic.equality.equals_reflexivity
45	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
46	instantiation	71, 59, 62	⊢
	: , : , :
47	instantiation	71, 60, 70	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
49	instantiation	61, 62	⊢
	:
50	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
51	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
52	theorem		⊢
	proveit.numbers.negation.negated_zero
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
54	instantiation	71, 63, 64	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
56	instantiation	71, 65, 66	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
58	instantiation	67, 68	⊢
	: , :
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
60	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
61	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
62	assumption		⊢
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
64	instantiation	71, 69, 70	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	71, 72, 73	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
70	instantiation	74, 75	⊢
	:
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
74	theorem		⊢
	proveit.numbers.negation.int_neg_closure
75	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1