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	reference	31	⊢
2	generalization	4	⊢
3	generalization	5	⊢
4	instantiation	20, 6, 7	⊢
	: , :
5	instantiation	13, 8, 9	, , ⊢
	: , : , :
6	instantiation	31, 10, 11	⊢
	: , :
7	instantiation	12	⊢
	: , : , : , :
8	instantiation	13, 14, 15	, , ⊢
	: , : , :
9	instantiation	23, 16	⊢
	: , : , :
10	axiom		⊢
	proveit.logic.booleans.true_axiom
11	assumption		⊢
12	instantiation	34, 51, 17^, 18^, 19^*	⊢
	:
13	theorem		⊢
	proveit.logic.equality.sub_right_side_into
14	instantiation	20, 21, 22	, , ⊢
	: , :
15	instantiation	23, 24	⊢
	: , : , :
16	instantiation	72, 73	⊢
	: , :
17	instantiation	26, 51, 80, 52, 25, 39	⊢
	: , : , : , : , : , : , :
18	instantiation	26, 51, 80, 52, 27, 40	⊢
	: , : , : , : , : , : , :
19	instantiation	28, 29, 30	⊢
	: , : , :
20	theorem		⊢
	proveit.logic.equality.lhs_via_equality
21	instantiation	31, 32, 33	, , ⊢
	: , :
22	instantiation	34, 73	⊢
	: , : , : , : , :
23	theorem		⊢
	proveit.core_expr_types.tuples.merge_extension
24	instantiation	72, 73	⊢
	: , :
25	instantiation	64, 51	⊢
	: , :
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_portion_substitution
27	instantiation	64, 51	⊢
	: , :
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	35, 36, 37, 38, 39, 40	⊢
	: , : , : , :
30	instantiation	41, 42	⊢
	:
31	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
32	instantiation	43, 44	, , ⊢
	: , :
33	instantiation	45, 73, 51, 53, 52, 54	, ⊢
	: , : , : , : , :
34	axiom		⊢
	proveit.core_expr_types.tuples.tuple_eq_def
35	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
37	instantiation	46	⊢
	: , :
38	instantiation	46	⊢
	: , :
39	instantiation	47, 48	⊢
	: , : , :
40	instantiation	47, 48	⊢
	: , : , :
41	axiom		⊢
	proveit.logic.booleans.eq_true_intro
42	instantiation	49	⊢
	:
43	assumption		⊢
44	instantiation	50, 51, 73, 80, 52, 53, 54	, ⊢
	: , : , : , : , : , :
45	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47	axiom		⊢
	proveit.core_expr_types.tuples.empty_range_def
48	instantiation	55, 56	⊢
	:
49	axiom		⊢
	proveit.logic.equality.equals_reflexivity
50	theorem		⊢
	proveit.logic.booleans.conjunction.some_from_and
51	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
52	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
53	instantiation	64, 73	⊢
	: , :
54	instantiation	57, 65, 58, 59, 60, 61	, ⊢
	: , : , : , :
55	theorem		⊢
	proveit.numbers.addition.elim_zero_left
56	instantiation	78, 62, 63	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.equality.sub_in_right_operands_via_tuple
58	instantiation	64, 65	⊢
	: , :
59	instantiation	66, 73	⊢
	: , : , :
60	assumption		⊢
61	instantiation	67, 68	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
63	instantiation	78, 69, 70	⊢
	: , : , :
64	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
65	instantiation	71, 73, 80	⊢
	: , :
66	theorem		⊢
	proveit.core_expr_types.tuples.extended_range_from1_len_typical_eq
67	axiom		⊢
	proveit.core_expr_types.tuples.range_extension_def
68	instantiation	72, 73	⊢
	: , :
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
70	instantiation	78, 74, 75	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
72	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_is_nat
73	instantiation	78, 76, 77	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
75	instantiation	78, 79, 80	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
77	assumption		⊢
78	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements