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	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
2	instantiation	76, 66, 4	⊢
	: , : , :
3	instantiation	5, 6, 7	⊢
	: , : , :
4	instantiation	76, 71, 8	⊢
	: , : , :
5	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
6	instantiation	9, 19, 10	⊢
	: , : , :
7	instantiation	41, 11, 12	⊢
	: , : , :
8	instantiation	62, 63, 13	⊢
	: , :
9	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
10	instantiation	14, 70, 55, 45	⊢
	: , : , :
11	instantiation	15, 16, 17, 59, 18, 19	⊢
	: , : , :
12	instantiation	20, 21, 22	⊢
	: , : , :
13	instantiation	76, 23, 24	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
15	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
16	instantiation	76, 66, 25	⊢
	: , : , :
17	instantiation	76, 66, 26	⊢
	: , : , :
18	instantiation	27, 70, 55, 45	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	28, 31, 78, 73, 33, 29, 34, 53, 52	⊢
	: , : , : , : , : , :
22	instantiation	30, 73, 78, 31, 32, 33, 34, 53, 52, 35^*	⊢
	: , : , : , : , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
24	instantiation	36, 37	⊢
	:
25	instantiation	76, 71, 38	⊢
	: , : , :
26	instantiation	76, 71, 55	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
28	theorem		⊢
	proveit.numbers.addition.disassociation
29	instantiation	39	⊢
	: , :
30	theorem		⊢
	proveit.numbers.addition.association
31	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
32	instantiation	39	⊢
	: , :
33	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
34	instantiation	76, 60, 40	⊢
	: , : , :
35	instantiation	41, 42, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.negation.int_neg_closure
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
38	instantiation	76, 44, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	instantiation	46, 47, 69	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.equality.sub_right_side_into
42	instantiation	48, 52, 49, 50	⊢
	: , : , :
43	instantiation	51, 52, 53	⊢
	: , :
44	instantiation	54, 70, 55	⊢
	: , :
45	assumption		⊢
46	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
47	instantiation	56, 57	⊢
	: , :
48	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
49	instantiation	76, 60, 58	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
51	theorem		⊢
	proveit.numbers.addition.commutation
52	instantiation	76, 60, 59	⊢
	: , : , :
53	instantiation	76, 60, 61	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
55	instantiation	62, 63, 72	⊢
	: , :
56	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
58	instantiation	76, 66, 64	⊢
	: , : , :
59	instantiation	76, 66, 65	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
61	instantiation	76, 66, 67	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
63	instantiation	76, 68, 69	⊢
	: , : , :
64	instantiation	76, 71, 75	⊢
	: , : , :
65	instantiation	76, 71, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
67	instantiation	76, 71, 72	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
69	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
70	instantiation	76, 77, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	instantiation	74, 75	⊢
	:
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
74	theorem		⊢
	proveit.numbers.negation.int_closure
75	instantiation	76, 77, 78	⊢
	: , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements