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, 5, 6	⊢
	: , : , : , :
1	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
2	reference	26	⊢
3	instantiation	36	⊢
	: , : , :
4	instantiation	36	⊢
	: , : , :
5	instantiation	7, 46, 8	⊢
	: , : , :
6	instantiation	9, 10, 11	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
8	instantiation	12	⊢
	:
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	13, 14	⊢
	: , : , :
11	instantiation	15, 16, 17, 18	⊢
	: , : , : , :
12	axiom		⊢
	proveit.logic.equality.equals_reflexivity
13	axiom		⊢
	proveit.logic.equality.substitution
14	instantiation	19, 20, 53, 21^*	⊢
	: , :
15	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
16	instantiation	22, 66, 71, 23, 24, 35, 47, 46	⊢
	: , : , : , : , : , :
17	instantiation	25, 29, 26, 31, 27, 35, 47, 46	⊢
	: , : , : , :
18	instantiation	28, 66, 71, 29, 30, 31, 35, 47, 46, 32^*	⊢
	: , : , : , : , : , :
19	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
20	instantiation	69, 59, 33	⊢
	: , : , :
21	instantiation	34, 35	⊢
	:
22	theorem		⊢
	proveit.numbers.addition.disassociation
23	instantiation	37	⊢
	: , :
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
25	theorem		⊢
	proveit.numbers.addition.elim_zero_any
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
27	instantiation	36	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.association
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	instantiation	37	⊢
	: , :
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	instantiation	38, 39, 40	⊢
	: , : , :
33	instantiation	69, 64, 41	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.negation.double_negation
35	instantiation	69, 59, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
38	theorem		⊢
	proveit.logic.equality.sub_right_side_into
39	instantiation	43, 46, 53, 44	⊢
	: , : , :
40	instantiation	45, 46, 47	⊢
	: , :
41	instantiation	69, 67, 48	⊢
	: , : , :
42	instantiation	49, 50, 62	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
44	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
45	theorem		⊢
	proveit.numbers.addition.commutation
46	instantiation	69, 59, 51	⊢
	: , : , :
47	instantiation	52, 53	⊢
	:
48	instantiation	54, 55	⊢
	:
49	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
50	instantiation	56, 57	⊢
	: , :
51	instantiation	69, 64, 58	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.negation.complex_closure
53	instantiation	69, 59, 60	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.negation.int_closure
55	instantiation	69, 61, 62	⊢
	: , : , :
56	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
58	instantiation	69, 67, 63	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
60	instantiation	69, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
62	assumption		⊢
63	instantiation	69, 70, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
65	instantiation	69, 67, 68	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
68	instantiation	69, 70, 71	⊢
	: , : , :
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements