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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.inclusion.fold_subset_eq
2	generalization	3	⊢
3	instantiation	4, 54, 5, 52, 6	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOO
5	instantiation	74, 64, 7	⊢
	: , : , :
6	instantiation	8, 9, 10	⊢
	: , :
7	instantiation	74, 69, 11	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
9	instantiation	12, 13, 58, 14, 15, 16^, 17^	⊢
	: , : , :
10	instantiation	34, 18, 19	⊢
	: , : , :
11	instantiation	74, 75, 20	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
13	instantiation	21, 56	⊢
	:
14	instantiation	22, 52, 56	⊢
	: , :
15	instantiation	30, 58, 52, 56, 23, 32	⊢
	: , : , :
16	instantiation	24, 48, 51, 25, 26	⊢
	: , : , :
17	instantiation	27, 28, 29	⊢
	: , : , :
18	instantiation	30, 52, 59, 56, 31, 32	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
21	theorem		⊢
	proveit.numbers.negation.real_closure
22	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
23	instantiation	33, 58, 59, 60	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
25	instantiation	74, 55, 58	⊢
	: , : , :
26	instantiation	34, 35, 36	⊢
	: , : , :
27	axiom		⊢
	proveit.logic.equality.equals_transitivity
28	instantiation	37, 38, 71, 72, 39, 40, 43, 51, 41	⊢
	: , : , : , : , : , :
29	instantiation	42, 51, 43, 44	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.ordering.less_add_right
31	instantiation	45, 58, 59, 60	⊢
	: , : , :
32	instantiation	46, 72	⊢
	:
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_lower_bound
34	theorem		⊢
	proveit.logic.equality.sub_right_side_into
35	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
36	instantiation	47, 51, 48	⊢
	: , :
37	theorem		⊢
	proveit.numbers.addition.disassociation
38	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
39	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
40	instantiation	49	⊢
	: , :
41	instantiation	50, 51	⊢
	:
42	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
43	instantiation	74, 55, 52	⊢
	: , : , :
44	instantiation	53	⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_upper_bound
46	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
47	theorem		⊢
	proveit.numbers.addition.commutation
48	instantiation	74, 55, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
50	theorem		⊢
	proveit.numbers.negation.complex_closure
51	instantiation	74, 55, 56	⊢
	: , : , :
52	instantiation	57, 58, 59, 60	⊢
	: , : , :
53	axiom		⊢
	proveit.logic.equality.equals_reflexivity
54	instantiation	74, 64, 61	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
56	instantiation	74, 64, 62	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real
58	instantiation	74, 64, 63	⊢
	: , : , :
59	instantiation	74, 64, 65	⊢
	: , : , :
60	assumption		⊢
61	instantiation	74, 69, 66	⊢
	: , : , :
62	instantiation	74, 69, 67	⊢
	: , : , :
63	instantiation	74, 69, 68	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
65	instantiation	74, 69, 70	⊢
	: , : , :
66	instantiation	74, 75, 71	⊢
	: , : , :
67	instantiation	74, 75, 72	⊢
	: , : , :
68	instantiation	74, 75, 73	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
70	instantiation	74, 75, 76	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
74	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements