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