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, 5	, , , , , , , , , ⊢
	: , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_factorization
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
3	instantiation	6, 7, 8	, , , ⊢
	: , : , :
4	instantiation	9	⊢
	: , : , : , :
5	instantiation	31, 10, 11	, , , , , ⊢
	: , : , :
6	theorem		⊢
	proveit.logic.equality.sub_right_side_into
7	instantiation	36, 22, 12	, , , ⊢
	: , :
8	instantiation	13, 14, 15	, , , ⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
10	instantiation	16, 17, 18	, , , , , ⊢
	: , :
11	instantiation	42, 19, 20	⊢
	: , : , :
12	instantiation	36, 29, 30	, ⊢
	: , :
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	23, 21, 25, 24, 28, 26, 22, 29, 30	, , , ⊢
	: , : , : , : , : , :
15	instantiation	23, 24, 25, 26, 27, 28, 37, 38, 29, 30	, , , ⊢
	: , : , : , : , : , :
16	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
17	instantiation	31, 32, 33	, , , , , ⊢
	: , : , :
18	instantiation	34, 54, 55	, ⊢
	: , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
20	instantiation	35	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
22	instantiation	36, 37, 38	, ⊢
	: , :
23	theorem		⊢
	proveit.numbers.multiplication.disassociation
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	47	⊢
	: , :
28	instantiation	47	⊢
	: , :
29	assumption		⊢
30	assumption		⊢
31	theorem		⊢
	proveit.logic.equality.sub_left_side_into
32	instantiation	39, 49, 50, 40, 41	, , , , , ⊢
	: , : , : , :
33	instantiation	42, 43, 44	⊢
	: , : , :
34	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
36	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
37	assumption		⊢
38	assumption		⊢
39	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
40	instantiation	45, 49, 50, 46	, , , , ⊢
	: , : , :
41	assumption		⊢
42	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
44	instantiation	47	⊢
	: , :
45	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
46	instantiation	48, 49, 54, 50, 51, 52	, , , , ⊢
	: , : , : , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
48	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
49	instantiation	58, 66	⊢
	:
50	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
51	instantiation	53, 54, 55	, ⊢
	: , :
52	instantiation	56, 65, 66, 57	, , , ⊢
	: , : , :
53	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
54	instantiation	58, 65	⊢
	:
55	assumption		⊢
56	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
57	modus ponens	59, 60	, , , ⊢
58	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
59	instantiation	61, 71, 62, 63	, , ⊢
	: , : , : , : , : , :
60	assumption		⊢
61	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
62	instantiation	64, 65, 66	, ⊢
	: , :
63	instantiation	67, 68	⊢
	: , :
64	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
65	assumption		⊢
66	assumption		⊢
67	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
68	instantiation	69, 70, 71	⊢
	: , : , :
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
71	assumption		⊢