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	33	⊢
2	instantiation	19, 4	⊢
	: , : , :
3	instantiation	5, 6, 7^*	, ⊢
	:
4	instantiation	33, 8, 9	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
6	instantiation	10, 11	, ⊢
	: , :
7	instantiation	12, 44, 47, 13^*	⊢
	: , :
8	instantiation	19, 14	⊢
	: , : , :
9	instantiation	15, 46, 47	⊢
	: , :
10	theorem		⊢
	proveit.numbers.ordering.relax_less
11	instantiation	16, 17	, ⊢
	: , :
12	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_subtract
13	instantiation	18, 46	⊢
	:
14	instantiation	19, 20	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
16	theorem		⊢
	proveit.numbers.addition.subtraction.neg_difference
17	instantiation	21, 50, 29, 22, 23, 24^, 25^	, ⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.negation.double_negation
19	axiom		⊢
	proveit.logic.equality.substitution
20	instantiation	26, 30	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
22	instantiation	64, 57, 27	⊢
	: , : , :
23	instantiation	28, 29, 51, 53, 30, 31	⊢
	: , : , :
24	instantiation	32, 44	⊢
	:
25	instantiation	33, 34, 35	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
27	assumption		⊢
28	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
30	instantiation	36, 61	⊢
	:
31	instantiation	37, 38	⊢
	:
32	theorem		⊢
	proveit.numbers.addition.elim_zero_left
33	axiom		⊢
	proveit.logic.equality.equals_transitivity
34	instantiation	39, 40, 66, 41, 42, 43, 46, 47, 44	⊢
	: , : , : , : , : , :
35	instantiation	45, 46, 47, 48	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	theorem		⊢
	proveit.numbers.addition.disassociation
40	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
42	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
43	instantiation	49	⊢
	: , :
44	instantiation	64, 52, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
46	instantiation	64, 52, 51	⊢
	: , : , :
47	instantiation	64, 52, 53	⊢
	: , : , :
48	instantiation	54	⊢
	:
49	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
50	instantiation	64, 55, 56	⊢
	: , : , :
51	instantiation	64, 57, 61	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
53	instantiation	64, 58, 59	⊢
	: , : , :
54	axiom		⊢
	proveit.logic.equality.equals_reflexivity
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonpos_within_real
56	instantiation	60, 61	⊢
	:
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	64, 62, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.negation.real_nonpos_closure
61	assumption		⊢
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
63	instantiation	64, 65, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements