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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5	, ⊢
	: , : , :
3	instantiation	6, 7	, ⊢
	:
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 44, 29, 30, 9, 31, 10, 11, 12, 13, 14^*	, ⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
7	instantiation	15, 16	, ⊢
	:
8	theorem		⊢
	proveit.numbers.addition.association
9	instantiation	39	⊢
	: , :
10	instantiation	47, 20, 17	⊢
	: , : , :
11	instantiation	47, 20, 18	⊢
	: , : , :
12	instantiation	47, 20, 19	⊢
	: , : , :
13	instantiation	47, 20, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
16	instantiation	47, 22, 23	, ⊢
	: , : , :
17	instantiation	47, 24, 32	⊢
	: , : , :
18	instantiation	47, 24, 33	⊢
	: , : , :
19	instantiation	47, 26, 25	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
21	instantiation	47, 26, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonneg
23	instantiation	28, 44, 29, 30, 31, 32, 33, 34, 35	, ⊢
	: , : , : , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
25	instantiation	47, 37, 36	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
27	instantiation	47, 37, 38	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.add_real_pos_from_nonneg
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	instantiation	39	⊢
	: , :
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	assumption		⊢
33	assumption		⊢
34	instantiation	47, 40, 41	⊢
	: , : , :
35	instantiation	42, 43	⊢
	:
36	instantiation	47, 45, 44	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
38	instantiation	47, 45, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
41	instantiation	47, 48, 49	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
^*equality replacement requirements