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	9	⊢
2	instantiation	4, 63, 5, 6, 7, 8	⊢
	: , : , : , :
3	instantiation	9, 10, 11	⊢
	: , : , :
4	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
5	instantiation	27	⊢
	: , :
6	instantiation	27	⊢
	: , :
7	instantiation	12, 34, 23	⊢
	: , : , :
8	instantiation	13, 58, 63, 17, 14, 19, 22, 35, 34, 15^*	⊢
	: , : , : , : , : , :
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	16, 58, 63, 17, 18, 19, 34, 22, 20	⊢
	: , : , : , : , : , :
11	instantiation	21, 34, 22, 23	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
13	theorem		⊢
	proveit.numbers.addition.association
14	instantiation	27	⊢
	: , :
15	instantiation	24, 25, 26	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.disassociation
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	instantiation	27	⊢
	: , :
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	61, 49, 28	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
22	instantiation	61, 49, 29	⊢
	: , : , :
23	instantiation	30	⊢
	:
24	theorem		⊢
	proveit.logic.equality.sub_right_side_into
25	instantiation	31, 34, 43, 32	⊢
	: , : , :
26	instantiation	33, 34, 35	⊢
	: , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	instantiation	61, 36, 37	⊢
	: , : , :
29	instantiation	38, 39, 40	⊢
	: , : , :
30	axiom		⊢
	proveit.logic.equality.equals_reflexivity
31	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
33	theorem		⊢
	proveit.numbers.addition.commutation
34	instantiation	61, 49, 41	⊢
	: , : , :
35	instantiation	42, 43	⊢
	:
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
37	instantiation	61, 44, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
39	instantiation	46, 47	⊢
	: , :
40	assumption		⊢
41	instantiation	61, 54, 48	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.negation.complex_closure
43	instantiation	61, 49, 50	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
45	instantiation	61, 51, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
48	instantiation	61, 59, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	61, 54, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
52	instantiation	56, 57	⊢
	:
53	instantiation	61, 62, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
55	instantiation	61, 59, 60	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.negation.int_neg_closure
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
60	instantiation	61, 62, 63	⊢
	: , : , :
61	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements