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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
2	reference	53	⊢
3	instantiation	73, 63, 6	⊢
	: , : , :
4	reference	51	⊢
5	instantiation	7, 8, 9	⊢
	: , :
6	instantiation	73, 68, 10	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
8	instantiation	11, 12, 57, 13, 14, 15^, 16^	⊢
	: , : , :
9	instantiation	33, 17, 18	⊢
	: , : , :
10	instantiation	73, 74, 19	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
12	instantiation	20, 55	⊢
	:
13	instantiation	21, 51, 55	⊢
	: , :
14	instantiation	29, 57, 51, 55, 22, 31	⊢
	: , : , :
15	instantiation	23, 47, 50, 24, 25	⊢
	: , : , :
16	instantiation	26, 27, 28	⊢
	: , : , :
17	instantiation	29, 51, 58, 55, 30, 31	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
20	theorem		⊢
	proveit.numbers.negation.real_closure
21	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
22	instantiation	32, 57, 58, 59	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
24	instantiation	73, 54, 57	⊢
	: , : , :
25	instantiation	33, 34, 35	⊢
	: , : , :
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	36, 37, 70, 71, 38, 39, 42, 50, 40	⊢
	: , : , : , : , : , :
28	instantiation	41, 50, 42, 43	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.ordering.less_add_right
30	instantiation	44, 57, 58, 59	⊢
	: , : , :
31	instantiation	45, 71	⊢
	:
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_lower_bound
33	theorem		⊢
	proveit.logic.equality.sub_right_side_into
34	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
35	instantiation	46, 50, 47	⊢
	: , :
36	theorem		⊢
	proveit.numbers.addition.disassociation
37	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
38	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
39	instantiation	48	⊢
	: , :
40	instantiation	49, 50	⊢
	:
41	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
42	instantiation	73, 54, 51	⊢
	: , : , :
43	instantiation	52	⊢
	:
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_upper_bound
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
46	theorem		⊢
	proveit.numbers.addition.commutation
47	instantiation	73, 54, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
49	theorem		⊢
	proveit.numbers.negation.complex_closure
50	instantiation	73, 54, 55	⊢
	: , : , :
51	instantiation	56, 57, 58, 59	⊢
	: , : , :
52	axiom		⊢
	proveit.logic.equality.equals_reflexivity
53	instantiation	73, 63, 60	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	73, 63, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real
57	instantiation	73, 63, 62	⊢
	: , : , :
58	instantiation	73, 63, 64	⊢
	: , : , :
59	assumption		⊢
60	instantiation	73, 68, 65	⊢
	: , : , :
61	instantiation	73, 68, 66	⊢
	: , : , :
62	instantiation	73, 68, 67	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
64	instantiation	73, 68, 69	⊢
	: , : , :
65	instantiation	73, 74, 70	⊢
	: , : , :
66	instantiation	73, 74, 71	⊢
	: , : , :
67	instantiation	73, 74, 72	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
69	instantiation	73, 74, 75	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
73	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements