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