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