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, 6^*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
2	reference	51	⊢
3	instantiation	7, 38	⊢
	:
4	instantiation	8, 61, 36	⊢
	: , :
5	instantiation	9, 36, 57, 38, 10, 11, 12^, 13^	⊢
	: , : , :
6	instantiation	32, 14, 15	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.negation.real_closure
8	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
9	theorem		⊢
	proveit.numbers.multiplication.reversed_weak_bound_via_right_factor_bound
10	instantiation	16, 74, 81, 65	⊢
	: , : , :
11	instantiation	17, 18	⊢
	: , :
12	instantiation	20, 43, 31, 19^*	⊢
	: , :
13	instantiation	20, 43, 49, 21^*	⊢
	: , :
14	instantiation	22, 83, 23, 24, 25, 26, 43, 53, 27	⊢
	: , : , : , : , : , :
15	instantiation	28, 43, 53, 29	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
17	theorem		⊢
	proveit.numbers.ordering.relax_less
18	instantiation	30, 63	⊢
	:
19	instantiation	48, 31	⊢
	:
20	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
21	instantiation	32, 33, 34	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.addition.disassociation
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	instantiation	35	⊢
	: , :
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	84, 60, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
29	instantiation	37	⊢
	:
30	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
31	instantiation	84, 60, 38	⊢
	: , : , :
32	axiom		⊢
	proveit.logic.equality.equals_transitivity
33	instantiation	39, 40	⊢
	: , : , :
34	instantiation	41, 42, 43, 44^*	⊢
	: , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	instantiation	84, 45, 46	⊢
	: , : , :
37	axiom		⊢
	proveit.logic.equality.equals_reflexivity
38	instantiation	84, 66, 47	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.substitution
40	instantiation	48, 49	⊢
	:
41	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
42	instantiation	84, 60, 50	⊢
	: , : , :
43	instantiation	84, 60, 51	⊢
	: , : , :
44	instantiation	52, 53	⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
46	instantiation	84, 54, 55	⊢
	: , : , :
47	instantiation	84, 73, 56	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
49	instantiation	84, 60, 57	⊢
	: , : , :
50	instantiation	84, 66, 58	⊢
	: , : , :
51	instantiation	84, 66, 59	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.negation.double_negation
53	instantiation	84, 60, 61	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
55	instantiation	84, 62, 63	⊢
	: , : , :
56	instantiation	84, 64, 65	⊢
	: , : , :
57	instantiation	84, 66, 67	⊢
	: , : , :
58	instantiation	84, 73, 78	⊢
	: , : , :
59	instantiation	84, 73, 79	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
61	instantiation	68, 69, 86	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
63	instantiation	70, 71	⊢
	:
64	instantiation	72, 74, 81	⊢
	: , :
65	assumption		⊢
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
67	instantiation	84, 73, 74	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
69	instantiation	75, 76	⊢
	: , :
70	theorem		⊢
	proveit.numbers.negation.int_neg_closure
71	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
72	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
74	instantiation	77, 78, 79	⊢
	: , :
75	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
77	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
78	instantiation	80, 81	⊢
	:
79	instantiation	84, 82, 83	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.negation.int_closure
81	instantiation	84, 85, 86	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
84	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
85	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
86	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
^*equality replacement requirements