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	⊢
	: , : , :
1	axiom		⊢
	proveit.linear_algebra.tensors.unary_tensor_prod_def
2	reference	18	⊢
3	instantiation	17, 18, 4, 5	⊢
	: , : , : , :
4	instantiation	6, 7, 8, 9	⊢
	: , :
5	instantiation	10, 18, 11, 12	⊢
	: , : , : , :
6	theorem		⊢
	proveit.numbers.division.div_complex_closure
7	instantiation	68, 60, 13	⊢
	: , : , :
8	instantiation	14, 55	⊢
	:
9	instantiation	15, 24, 16	⊢
	: , :
10	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
11	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
12	instantiation	17, 18, 19, 20	⊢
	: , : , : , :
13	instantiation	68, 62, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
15	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
16	instantiation	22, 23, 24	⊢
	: , :
17	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
18	instantiation	25, 39	⊢
	:
19	instantiation	26, 27, 28	⊢
	: , :
20	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
21	instantiation	68, 66, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
23	instantiation	68, 31, 30	⊢
	: , : , :
24	instantiation	68, 31, 32	⊢
	: , : , :
25	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
26	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
27	instantiation	68, 60, 33	⊢
	: , : , :
28	instantiation	34, 35, 36	⊢
	: , : , :
29	instantiation	68, 69, 45	⊢
	: , : , :
30	instantiation	68, 38, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
32	instantiation	68, 38, 39	⊢
	: , : , :
33	instantiation	68, 64, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.equality.sub_right_side_into
35	instantiation	54, 46, 41	⊢
	: , :
36	instantiation	42, 43, 44	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
41	instantiation	54, 52, 53	⊢
	: , :
42	axiom		⊢
	proveit.logic.equality.equals_transitivity
43	instantiation	47, 45, 70, 48, 51, 49, 46, 52, 53	⊢
	: , : , : , : , : , :
44	instantiation	47, 48, 70, 49, 50, 51, 55, 56, 52, 53	⊢
	: , : , : , : , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
46	instantiation	54, 55, 56	⊢
	: , :
47	theorem		⊢
	proveit.numbers.multiplication.disassociation
48	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
49	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
50	instantiation	57	⊢
	: , :
51	instantiation	57	⊢
	: , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
53	instantiation	68, 60, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
55	instantiation	68, 60, 59	⊢
	: , : , :
56	instantiation	68, 60, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
58	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
59	instantiation	68, 62, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
61	instantiation	68, 64, 65	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
63	instantiation	68, 66, 67	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
67	instantiation	68, 69, 70	⊢
	: , : , :
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.nat2