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^*	⊢
	: , : , : , : , : , :
1	reference	23	⊢
2	reference	24	⊢
3	reference	38	⊢
4	reference	47	⊢
5	reference	25	⊢
6	reference	15	⊢
7	instantiation	10	⊢
	: , : , :
8	reference	28	⊢
9	instantiation	35, 11, 12	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
11	instantiation	42, 13	⊢
	: , : , :
12	instantiation	23, 24, 38, 25, 14, 15, 16, 28, 17^*	⊢
	: , : , : , : , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
14	instantiation	31	⊢
	: , :
15	instantiation	31	⊢
	: , :
16	instantiation	48, 33, 18	⊢
	: , : , :
17	instantiation	35, 19, 20	⊢
	: , : , :
18	instantiation	48, 40, 21	⊢
	: , : , :
19	instantiation	42, 22	⊢
	: , : , :
20	instantiation	23, 24, 38, 50, 25, 26, 27, 28, 29^*	⊢
	: , : , : , : , : , :
21	instantiation	48, 45, 30	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
23	theorem		⊢
	proveit.numbers.addition.association
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
26	instantiation	31	⊢
	: , :
27	instantiation	48, 33, 32	⊢
	: , : , :
28	instantiation	48, 33, 34	⊢
	: , : , :
29	instantiation	35, 36, 37	⊢
	: , : , :
30	instantiation	48, 49, 38	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32	instantiation	48, 40, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	48, 40, 41	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	42, 43	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
39	instantiation	48, 45, 44	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	48, 45, 46	⊢
	: , : , :
42	axiom		⊢
	proveit.logic.equality.substitution
43	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
44	instantiation	48, 49, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	48, 49, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements