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^*	⊢
	: , : , :
1	reference	38	⊢
2	instantiation	38, 5, 6	⊢
	: , : , :
3	instantiation	20, 7	⊢
	: , :
4	instantiation	38, 8, 9	⊢
	: , : , :
5	instantiation	38, 10, 11	⊢
	: , : , :
6	instantiation	44, 12	⊢
	: , : , :
7	instantiation	13, 66, 14, 25, 15, 26, 35, 31, 33, 47, 29, 16^*	⊢
	: , : , : , : , : , :
8	instantiation	44, 17	⊢
	: , : , :
9	instantiation	32, 35, 48	⊢
	: , :
10	instantiation	44, 18	⊢
	: , : , :
11	instantiation	44, 19	⊢
	: , : , :
12	instantiation	20, 21	⊢
	: , :
13	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
15	instantiation	22	⊢
	: , : , : , :
16	instantiation	23, 35	⊢
	:
17	instantiation	24, 25, 61, 26, 27, 28, 31, 33, 47, 29, 30^*	⊢
	: , : , : , : , : , :
18	instantiation	32, 31, 35	⊢
	: , :
19	instantiation	32, 33, 35	⊢
	: , :
20	theorem		⊢
	proveit.logic.equality.equals_reversal
21	instantiation	34, 35	⊢
	:
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
23	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
24	theorem		⊢
	proveit.numbers.addition.association
25	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	36	⊢
	: , :
28	instantiation	36	⊢
	: , :
29	instantiation	37, 47	⊢
	:
30	instantiation	38, 39, 40	⊢
	: , : , :
31	instantiation	67, 53, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.multiplication.commutation
33	instantiation	67, 53, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.negation.mult_neg_one_right
35	instantiation	67, 53, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	theorem		⊢
	proveit.numbers.negation.complex_closure
38	axiom		⊢
	proveit.logic.equality.equals_transitivity
39	instantiation	44, 45	⊢
	: , : , :
40	instantiation	46, 47, 48, 49	⊢
	: , : , :
41	instantiation	67, 59, 50	⊢
	: , : , :
42	instantiation	67, 59, 51	⊢
	: , : , :
43	assumption		⊢
44	axiom		⊢
	proveit.logic.equality.substitution
45	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
46	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
47	instantiation	67, 53, 52	⊢
	: , : , :
48	instantiation	67, 53, 54	⊢
	: , : , :
49	instantiation	55	⊢
	:
50	instantiation	67, 64, 56	⊢
	: , : , :
51	instantiation	67, 64, 57	⊢
	: , : , :
52	instantiation	67, 59, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
54	instantiation	67, 59, 60	⊢
	: , : , :
55	axiom		⊢
	proveit.logic.equality.equals_reflexivity
56	instantiation	67, 68, 61	⊢
	: , : , :
57	instantiation	67, 68, 62	⊢
	: , : , :
58	instantiation	67, 64, 63	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	67, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
63	instantiation	67, 68, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	67, 68, 69	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
^*equality replacement requirements