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	69, 52, 13	⊢
	: , : , :
12	instantiation	21, 14, 15	⊢
	: , : , :
13	instantiation	69, 49, 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, 71, 25, 30, 27, 31, 24, 37, 38, 33	⊢
	: , : , : , : , : , :
20	instantiation	29, 30, 61, 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, 61, 71, 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	69, 52, 40	⊢
	: , : , :
34	instantiation	69, 52, 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	instantiation	45, 46, 47, 48	⊢
	: , : , :
41	instantiation	69, 49, 50	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
43	instantiation	69, 52, 51	⊢
	: , : , :
44	instantiation	69, 52, 53	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
47	instantiation	69, 56, 54	⊢
	: , : , :
48	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
51	instantiation	69, 56, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
53	instantiation	69, 56, 57	⊢
	: , : , :
54	instantiation	69, 59, 68	⊢
	: , : , :
55	instantiation	69, 59, 58	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	69, 59, 60	⊢
	: , : , :
58	instantiation	69, 70, 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.numbers.addition.add_int_closure_bin
63	instantiation	69, 65, 66	⊢
	: , : , :
64	instantiation	67, 68	⊢
	:
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
66	assumption		⊢
67	theorem		⊢
	proveit.numbers.negation.int_closure
68	instantiation	69, 70, 71	⊢
	: , : , :
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat1