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	25	⊢
2	instantiation	5, 6, 7, 46, 47, 44	, ⊢
	: , :
3	reference	48	⊢
4	instantiation	14, 8, 9	, ⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.addition.add_real_closure
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
7	instantiation	10	⊢
	: , : , :
8	instantiation	23, 11	, ⊢
	: , : , :
9	instantiation	14, 12, 13	, ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
11	instantiation	14, 15, 16	, ⊢
	: , : , :
12	instantiation	17, 31, 56, 51, 32, 18, 20, 36, 21	, ⊢
	: , : , : , : , : , :
13	instantiation	30, 51, 56, 31, 19, 32, 20, 36, 21, 22^*	, ⊢
	: , : , : , : , : , :
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	23, 24	, ⊢
	: , : , :
16	instantiation	25, 40, 53	, ⊢
	: , :
17	theorem		⊢
	proveit.numbers.addition.disassociation
18	instantiation	42	⊢
	: , :
19	instantiation	42	⊢
	: , :
20	instantiation	26, 27, 28	, ⊢
	: , : , :
21	instantiation	54, 43, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
23	axiom		⊢
	proveit.logic.equality.substitution
24	instantiation	30, 31, 56, 51, 32, 33, 34, 35, 36	, ⊢
	: , : , : , : , : , :
25	theorem		⊢
	proveit.numbers.rounding.round_of_real_plus_int
26	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
27	instantiation	37, 38	⊢
	: , :
28	instantiation	39, 40	, ⊢
	:
29	instantiation	54, 49, 41	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.association
31	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
32	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
33	instantiation	42	⊢
	: , :
34	instantiation	54, 43, 46	⊢
	: , : , :
35	instantiation	54, 43, 47	⊢
	: , : , :
36	instantiation	54, 43, 44	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.int_within_complex
39	axiom		⊢
	proveit.numbers.rounding.round_is_an_int
40	instantiation	45, 46, 47	, ⊢
	: , :
41	instantiation	54, 52, 48	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	54, 49, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
46	assumption		⊢
47	assumption		⊢
48	instantiation	54, 55, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	54, 52, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	instantiation	54, 55, 56	⊢
	: , : , :
54	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements