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