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.addition.binary_closure
2	reference	6	⊢
3	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
4	instantiation	5, 6, 7, 8	, ⊢
	: , : , : , :
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
6	instantiation	9, 10	⊢
	:
7	instantiation	42, 11, 12	, ⊢
	: , :
8	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
9	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
11	instantiation	71, 51, 13	⊢
	: , : , :
12	instantiation	21, 14, 15	, ⊢
	: , : , :
13	instantiation	71, 45, 16	⊢
	: , : , :
14	instantiation	36, 24, 17	, ⊢
	: , :
15	instantiation	18, 19, 20	, ⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
17	instantiation	21, 22, 23	, ⊢
	: , : , :
18	axiom		⊢
	proveit.logic.equality.equals_transitivity
19	instantiation	29, 70, 25, 30, 27, 31, 24, 37, 38, 33	, ⊢
	: , : , : , : , : , :
20	instantiation	29, 30, 56, 25, 31, 26, 27, 43, 34, 37, 38, 33	, ⊢
	: , : , : , : , : , :
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	36, 28, 33	, ⊢
	: , :
23	instantiation	29, 30, 56, 70, 31, 32, 37, 38, 33	, ⊢
	: , : , : , : , : , :
24	instantiation	36, 43, 34	⊢
	: , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
26	instantiation	39	⊢
	: , :
27	instantiation	35	⊢
	: , : , :
28	instantiation	36, 37, 38	, ⊢
	: , :
29	theorem		⊢
	proveit.numbers.multiplication.disassociation
30	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	instantiation	39	⊢
	: , :
33	instantiation	71, 51, 40	⊢
	: , : , :
34	instantiation	71, 51, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
36	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
38	instantiation	42, 43, 44	, ⊢
	: , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
41	instantiation	71, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
43	instantiation	71, 51, 47	⊢
	: , : , :
44	instantiation	48, 49	, ⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
47	instantiation	71, 54, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.negation.complex_closure
49	instantiation	71, 51, 52	, ⊢
	: , : , :
50	instantiation	71, 57, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
52	instantiation	71, 54, 55	, ⊢
	: , : , :
53	instantiation	71, 69, 56	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
55	instantiation	71, 57, 58	, ⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
58	instantiation	71, 59, 60	, ⊢
	: , : , :
59	instantiation	61, 62, 63	⊢
	: , :
60	assumption		⊢
61	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
62	instantiation	64, 65, 66	⊢
	: , :
63	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
64	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
65	instantiation	67, 68	⊢
	:
66	instantiation	71, 69, 70	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.negation.int_closure
68	instantiation	71, 72, 73	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
73	assumption		⊢