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	reference	49	⊢
2	instantiation	4, 5, 8	, , , , , ⊢
	: , : , :
3	instantiation	15, 6, 7, 8	, , , , , ⊢
	: , : , : , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	49, 9, 10	, , , , , ⊢
	: , : , :
6	instantiation	11, 28, 12, 31, 13, 14	, , , , , ⊢
	: , : , : , : , : , :
7	instantiation	15, 16, 17, 18	, , , , , ⊢
	: , : , : , :
8	instantiation	19, 57, 42, 33, 34	, , , , , ⊢
	: , : , :
9	instantiation	53, 65, 66, 20, 55	, , , , , ⊢
	: , : , : , :
10	instantiation	56, 57, 21	⊢
	: , : , :
11	theorem		⊢
	proveit.physics.quantum.algebra.qmult_disassociation
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
13	instantiation	62	⊢
	: , :
14	instantiation	49, 22, 23	, , , , , ⊢
	: , : , :
15	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
16	instantiation	27, 24, 25, 59, 39, 26, 44	, , , , , ⊢
	: , : , : , : , :
17	instantiation	27, 28, 31, 64, 33, 29	, , , , , ⊢
	: , : , : , : , :
18	instantiation	30, 57, 31, 32, 64, 59, 33, 34	, , , , , ⊢
	: , : , : , :
19	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_factorization
20	instantiation	60, 65, 66, 35	, , , , ⊢
	: , : , :
21	instantiation	62	⊢
	: , :
22	instantiation	36, 59, 37	, , , , , ⊢
	: , :
23	instantiation	56, 38, 39	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
25	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
29	instantiation	49, 40, 41	, , , , ⊢
	: , : , :
30	theorem		⊢
	proveit.physics.quantum.algebra.qmult_scalar_association
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
32	instantiation	62	⊢
	: , :
33	instantiation	62	⊢
	: , :
34	instantiation	53, 65, 66, 67, 55	, , , ⊢
	: , : , : , :
35	instantiation	63, 42, 65, 66, 67	, , , , ⊢
	: , : , : , :
36	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_right_closure
37	instantiation	43, 44	, , , , ⊢
	:
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
39	instantiation	45	⊢
	: , : , :
40	instantiation	53, 65, 66, 46, 55	, , , , ⊢
	: , : , : , :
41	instantiation	56, 57, 47	⊢
	: , : , :
42	instantiation	48, 64, 59	, ⊢
	: , :
43	theorem		⊢
	proveit.physics.quantum.algebra.qmult_nested_closure
44	instantiation	49, 50, 51	, , , , ⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
46	instantiation	60, 65, 66, 52	, , , ⊢
	: , : , :
47	instantiation	62	⊢
	: , :
48	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
49	theorem		⊢
	proveit.logic.equality.sub_left_side_into
50	instantiation	53, 65, 66, 54, 55	, , , , ⊢
	: , : , : , :
51	instantiation	56, 57, 58	⊢
	: , : , :
52	instantiation	63, 59, 65, 66, 67	, , , ⊢
	: , : , : , :
53	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
54	instantiation	60, 65, 66, 61	, , , ⊢
	: , : , :
55	assumption		⊢
56	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
58	instantiation	62	⊢
	: , :
59	assumption		⊢
60	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
61	instantiation	63, 64, 65, 66, 67	, , , ⊢
	: , : , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
63	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_op_closure
64	assumption		⊢
65	instantiation	68, 71	⊢
	:
66	instantiation	68, 70	⊢
	:
67	instantiation	69, 70, 71, 72	, , ⊢
	: , : , :
68	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
69	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
70	assumption		⊢
71	assumption		⊢
72	assumption		⊢