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, 7, 46, 53, 9, 5, 10, 22, 21	⊢
	: , : , : , : , : , :
3	instantiation	6, 53, 46, 7, 8, 9, 10, 22, 21, 11^*	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	instantiation	12	⊢
	: , :
6	theorem		⊢
	proveit.numbers.addition.association
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	instantiation	12	⊢
	: , :
9	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10	instantiation	44, 30, 13	⊢
	: , : , :
11	instantiation	14, 15, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	instantiation	44, 35, 17	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.sub_right_side_into
15	instantiation	18, 21, 26, 19	⊢
	: , : , :
16	instantiation	20, 21, 22	⊢
	: , :
17	instantiation	44, 39, 23	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
20	theorem		⊢
	proveit.numbers.addition.commutation
21	instantiation	44, 30, 24	⊢
	: , : , :
22	instantiation	25, 26	⊢
	:
23	instantiation	44, 27, 28	⊢
	: , : , :
24	instantiation	44, 35, 29	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.negation.complex_closure
26	instantiation	44, 30, 31	⊢
	: , : , :
27	instantiation	32, 40, 33	⊢
	: , :
28	assumption		⊢
29	instantiation	44, 39, 34	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	instantiation	44, 35, 36	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
33	instantiation	44, 37, 38	⊢
	: , : , :
34	instantiation	44, 45, 53	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	44, 39, 40	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
38	instantiation	41, 53, 42, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	44, 45, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
42	instantiation	47, 53, 48	⊢
	:
43	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
47	theorem		⊢
	proveit.numbers.numerals.decimals.n_in_digits
48	instantiation	49, 50, 51	⊢
	: , :
49	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
50	instantiation	52, 53	⊢
	:
51	instantiation	54, 55	⊢
	:
52	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
54	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
55	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
^*equality replacement requirements