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.linear_algebra.scalar_multiplication.scalar_mult_closure
2	instantiation	5, 6	⊢
	:
3	instantiation	40, 7, 8	, ⊢
	: , :
4	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
5	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
7	instantiation	69, 49, 9	⊢
	: , : , :
8	instantiation	17, 10, 11	, ⊢
	: , : , :
9	instantiation	69, 43, 12	⊢
	: , : , :
10	instantiation	33, 20, 13	, ⊢
	: , :
11	instantiation	14, 15, 16	, ⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
13	instantiation	17, 18, 19	, ⊢
	: , : , :
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	26, 68, 21, 27, 23, 28, 20, 34, 35, 30	, ⊢
	: , : , : , : , : , :
16	instantiation	26, 27, 54, 21, 28, 22, 23, 41, 24, 34, 35, 30	, ⊢
	: , : , : , : , : , :
17	theorem		⊢
	proveit.logic.equality.sub_right_side_into
18	instantiation	33, 25, 30	, ⊢
	: , :
19	instantiation	26, 27, 54, 68, 28, 29, 34, 35, 30	, ⊢
	: , : , : , : , : , :
20	instantiation	69, 49, 31	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
22	instantiation	36	⊢
	: , :
23	instantiation	32	⊢
	: , : , :
24	instantiation	69, 49, 39	⊢
	: , : , :
25	instantiation	33, 34, 35	, ⊢
	: , :
26	theorem		⊢
	proveit.numbers.multiplication.disassociation
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
29	instantiation	36	⊢
	: , :
30	instantiation	69, 49, 37	⊢
	: , : , :
31	instantiation	38, 45, 39	⊢
	: , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
33	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
35	instantiation	40, 41, 42	, ⊢
	: , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
38	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
39	instantiation	69, 43, 44	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
41	instantiation	69, 49, 45	⊢
	: , : , :
42	instantiation	46, 47	, ⊢
	:
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
45	instantiation	69, 52, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.negation.complex_closure
47	instantiation	69, 49, 50	, ⊢
	: , : , :
48	instantiation	69, 55, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	69, 52, 53	, ⊢
	: , : , :
51	instantiation	69, 67, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	69, 55, 56	, ⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	69, 57, 58	, ⊢
	: , : , :
57	instantiation	59, 60, 61	⊢
	: , :
58	assumption		⊢
59	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
60	instantiation	62, 63, 64	⊢
	: , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
62	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
63	instantiation	65, 66	⊢
	:
64	instantiation	69, 67, 68	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.negation.int_closure
66	instantiation	69, 70, 71	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
71	assumption		⊢