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