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	33	⊢
2	instantiation	29, 4	⊢
	: , : , :
3	instantiation	37, 64, 39, 38, 41, 40, 5, 44, 48	⊢
	: , : , : , : , : , :
4	instantiation	6, 7, 8, 9, 10, 11	⊢
	: , : , :
5	modus ponens	12, 13	⊢
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
7	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
8	instantiation	46	⊢
	: , :
9	instantiation	46	⊢
	: , :
10	instantiation	29, 14	⊢
	: , : , :
11	instantiation	50	⊢
	:
12	instantiation	15	⊢
	: , : , :
13	generalization	16	⊢
14	modus ponens	17, 18	⊢
15	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
16	instantiation	62, 51, 19	, ⊢
	: , : , :
17	instantiation	20, 21	⊢
	: , : , : , : , : , :
18	generalization	22	⊢
19	instantiation	62, 56, 23	, ⊢
	: , : , :
20	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
22	instantiation	29, 24	⊢
	: , : , :
23	instantiation	62, 60, 25	, ⊢
	: , : , :
24	instantiation	29, 26	⊢
	: , : , :
25	instantiation	62, 27, 28	, ⊢
	: , : , :
26	instantiation	29, 30	⊢
	: , : , :
27	instantiation	31, 61, 32	⊢
	: , :
28	assumption		⊢
29	axiom		⊢
	proveit.logic.equality.substitution
30	instantiation	33, 34, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
32	instantiation	62, 36, 55	⊢
	: , : , :
33	axiom		⊢
	proveit.logic.equality.equals_transitivity
34	instantiation	37, 38, 39, 64, 40, 41, 44, 48, 42	⊢
	: , : , : , : , : , :
35	instantiation	43, 48, 44, 45	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
37	theorem		⊢
	proveit.numbers.addition.disassociation
38	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
40	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
41	instantiation	46	⊢
	: , :
42	instantiation	47, 48	⊢
	:
43	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
44	instantiation	62, 51, 49	⊢
	: , : , :
45	instantiation	50	⊢
	:
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47	theorem		⊢
	proveit.numbers.negation.complex_closure
48	instantiation	62, 51, 52	⊢
	: , : , :
49	instantiation	53, 54, 55	⊢
	: , : , :
50	axiom		⊢
	proveit.logic.equality.equals_reflexivity
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
52	instantiation	62, 56, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
54	instantiation	58, 59	⊢
	: , :
55	assumption		⊢
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	62, 60, 61	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
61	instantiation	62, 63, 64	⊢
	: , : , :
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat1