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, 4	⊢
	: , : , : , :
1	reference	13	⊢
2	instantiation	17, 18, 44, 19^*	⊢
	: , :
3	instantiation	5	⊢
	:
4	instantiation	6, 7	⊢
	: , :
5	axiom		⊢
	proveit.logic.equality.equals_reflexivity
6	theorem		⊢
	proveit.logic.equality.equals_reversal
7	instantiation	8, 9, 10	⊢
	: , : , :
8	axiom		⊢
	proveit.logic.equality.equals_transitivity
9	instantiation	11, 12	⊢
	: , : , :
10	instantiation	13, 14, 15, 16	⊢
	: , : , : , :
11	axiom		⊢
	proveit.logic.equality.substitution
12	instantiation	17, 18, 51, 19^*	⊢
	: , :
13	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
14	instantiation	20, 64, 69, 21, 22, 33, 45, 44	⊢
	: , : , : , : , : , :
15	instantiation	23, 27, 24, 29, 25, 33, 45, 44	⊢
	: , : , : , :
16	instantiation	26, 64, 69, 27, 28, 29, 33, 45, 44, 30^*	⊢
	: , : , : , : , : , :
17	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
18	instantiation	67, 57, 31	⊢
	: , : , :
19	instantiation	32, 33	⊢
	:
20	theorem		⊢
	proveit.numbers.addition.disassociation
21	instantiation	35	⊢
	: , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
23	theorem		⊢
	proveit.numbers.addition.elim_zero_any
24	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
25	instantiation	34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.association
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	instantiation	35	⊢
	: , :
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	instantiation	36, 37, 38	⊢
	: , : , :
31	instantiation	67, 62, 39	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.negation.double_negation
33	instantiation	67, 57, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	theorem		⊢
	proveit.logic.equality.sub_right_side_into
37	instantiation	41, 44, 51, 42	⊢
	: , : , :
38	instantiation	43, 44, 45	⊢
	: , :
39	instantiation	67, 65, 46	⊢
	: , : , :
40	instantiation	47, 48, 60	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
42	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
43	theorem		⊢
	proveit.numbers.addition.commutation
44	instantiation	67, 57, 49	⊢
	: , : , :
45	instantiation	50, 51	⊢
	:
46	instantiation	52, 53	⊢
	:
47	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
48	instantiation	54, 55	⊢
	: , :
49	instantiation	67, 62, 56	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.negation.complex_closure
51	instantiation	67, 57, 58	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.negation.int_closure
53	instantiation	67, 59, 60	⊢
	: , : , :
54	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
56	instantiation	67, 65, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
58	instantiation	67, 62, 63	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
60	assumption		⊢
61	instantiation	67, 68, 64	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
63	instantiation	67, 65, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	67, 68, 69	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements