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