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	theorem		⊢
	proveit.numbers.numerals.decimals.range_2_expansion
2	instantiation	5, 37	⊢
	: , :
3	instantiation	56, 6, 7	⊢
	: , : , :
4	instantiation	56, 8, 9	⊢
	: , : , :
5	theorem		⊢
	proveit.logic.equality.equals_reversal
6	instantiation	62, 37	⊢
	: , : , :
7	instantiation	14, 10, 11, 12	⊢
	: , : , : , :
8	instantiation	62, 13	⊢
	: , : , :
9	instantiation	14, 15, 16, 17	⊢
	: , : , : , :
10	instantiation	25, 18, 50	⊢
	: , :
11	instantiation	27, 33, 19, 20, 21	⊢
	: , : , : , :
12	instantiation	44, 45, 70, 46, 47, 31, 50, 22^*	⊢
	: , : , : , : , : , :
13	instantiation	56, 23, 24	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
15	instantiation	25, 26, 50	⊢
	: , :
16	instantiation	27, 67, 28, 29, 30	⊢
	: , : , : , :
17	instantiation	44, 45, 70, 47, 31, 50, 32^*	⊢
	: , : , : , : , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
19	instantiation	38, 33	⊢
	: , :
20	instantiation	34	⊢
	: , : , :
21	instantiation	35	⊢
	:
22	instantiation	56, 36, 63	⊢
	: , : , :
23	instantiation	62, 37	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
25	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_expansion
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
27	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
28	instantiation	38, 67	⊢
	: , :
29	instantiation	39	⊢
	: , : , : , :
30	instantiation	40	⊢
	:
31	instantiation	52	⊢
	: , :
32	instantiation	56, 41, 42	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
35	theorem		⊢
	proveit.numbers.numerals.decimals.reduce_3_repeats
36	instantiation	62, 43	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
38	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
40	theorem		⊢
	proveit.numbers.numerals.decimals.reduce_4_repeats
41	instantiation	62, 43	⊢
	: , : , :
42	instantiation	44, 45, 70, 46, 47, 48, 49, 50, 51^*	⊢
	: , : , : , : , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
44	theorem		⊢
	proveit.numbers.multiplication.association
45	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
47	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
48	instantiation	52	⊢
	: , :
49	instantiation	68, 54, 53	⊢
	: , : , :
50	instantiation	68, 54, 55	⊢
	: , : , :
51	instantiation	56, 57, 58	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
53	instantiation	68, 60, 59	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	68, 60, 61	⊢
	: , : , :
56	axiom		⊢
	proveit.logic.equality.equals_transitivity
57	instantiation	62, 63	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
59	instantiation	68, 65, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
61	instantiation	68, 65, 66	⊢
	: , : , :
62	axiom		⊢
	proveit.logic.equality.substitution
63	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
64	instantiation	68, 69, 67	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	68, 69, 70	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements