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^*	⊢
	: , : , : , : , : , :
1	reference	33	⊢
2	reference	64	⊢
3	reference	40	⊢
4	reference	34	⊢
5	instantiation	25	⊢
	: , : , : , :
6	reference	35	⊢
7	instantiation	10, 11, 12	⊢
	: , :
8	reference	27	⊢
9	instantiation	13, 14, 15^*	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
11	instantiation	62, 46, 16	⊢
	: , : , :
12	instantiation	62, 46, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	instantiation	18, 34, 40, 64, 35, 19, 38, 27, 20^*	⊢
	: , : , : , : , : , :
15	instantiation	33, 34, 61, 35, 21, 38, 22^*	⊢
	: , : , : , : , : , :
16	instantiation	62, 54, 23	⊢
	: , : , :
17	instantiation	41, 42, 24	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
19	instantiation	25	⊢
	: , : , : , :
20	instantiation	26, 27	⊢
	:
21	instantiation	44	⊢
	: , :
22	instantiation	48, 28, 29	⊢
	: , : , :
23	instantiation	62, 59, 30	⊢
	: , : , :
24	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
27	instantiation	62, 46, 31	⊢
	: , : , :
28	instantiation	56, 32	⊢
	: , : , :
29	instantiation	33, 34, 61, 64, 35, 36, 37, 38, 39^*	⊢
	: , : , : , : , : , :
30	instantiation	62, 63, 40	⊢
	: , : , :
31	instantiation	41, 42, 43	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
33	theorem		⊢
	proveit.numbers.addition.association
34	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
35	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36	instantiation	44	⊢
	: , :
37	instantiation	62, 46, 45	⊢
	: , : , :
38	instantiation	62, 46, 47	⊢
	: , : , :
39	instantiation	48, 49, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
41	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
42	instantiation	51, 52	⊢
	: , :
43	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45	instantiation	62, 54, 53	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	62, 54, 55	⊢
	: , : , :
48	axiom		⊢
	proveit.logic.equality.equals_transitivity
49	instantiation	56, 57	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
51	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
53	instantiation	62, 59, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
55	instantiation	62, 59, 60	⊢
	: , : , :
56	axiom		⊢
	proveit.logic.equality.substitution
57	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
58	instantiation	62, 63, 61	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
60	instantiation	62, 63, 64	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements