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, 5, 6, 7, 8, 9, 10, 11, 12^*	⊢
	: , : , : , : , : , :
1	reference	24	⊢
2	reference	25	⊢
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
4	reference	48	⊢
5	reference	26	⊢
6	instantiation	13	⊢
	: , : , : , :
7	instantiation	14	⊢
	: , : , :
8	reference	29	⊢
9	reference	17	⊢
10	reference	28	⊢
11	assumption		⊢
12	instantiation	24, 25, 39, 26, 15, 16, 29, 17, 28, 18^*	⊢
	: , : , : , : , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
15	instantiation	32	⊢
	: , :
16	instantiation	32	⊢
	: , :
17	instantiation	49, 34, 19	⊢
	: , : , :
18	instantiation	36, 20, 21	⊢
	: , : , :
19	instantiation	49, 41, 22	⊢
	: , : , :
20	instantiation	43, 23	⊢
	: , : , :
21	instantiation	24, 25, 39, 51, 26, 27, 28, 29, 30^*	⊢
	: , : , : , : , : , :
22	instantiation	49, 46, 31	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
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	32	⊢
	: , :
28	instantiation	49, 34, 33	⊢
	: , : , :
29	instantiation	49, 34, 35	⊢
	: , : , :
30	instantiation	36, 37, 38	⊢
	: , : , :
31	instantiation	49, 50, 39	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33	instantiation	49, 41, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	49, 41, 42	⊢
	: , : , :
36	axiom		⊢
	proveit.logic.equality.equals_transitivity
37	instantiation	43, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.add_6_1
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
40	instantiation	49, 46, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	49, 46, 47	⊢
	: , : , :
43	axiom		⊢
	proveit.logic.equality.substitution
44	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_3
45	instantiation	49, 50, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	49, 50, 51	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements