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	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
2	instantiation	4, 5, 6	, , , , , ⊢
	: , : , :
3	instantiation	7, 23, 24	, ⊢
	: , :
4	theorem		⊢
	proveit.logic.equality.sub_left_side_into
5	instantiation	8, 18, 19, 9, 10	, , , , , ⊢
	: , : , : , :
6	instantiation	11, 12, 13	⊢
	: , : , :
7	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
8	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
9	instantiation	14, 18, 19, 15	, , , , ⊢
	: , : , :
10	assumption		⊢
11	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
13	instantiation	16	⊢
	: , :
14	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
15	instantiation	17, 18, 23, 19, 20, 21	, , , , ⊢
	: , : , : , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
18	instantiation	27, 35	⊢
	:
19	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
20	instantiation	22, 23, 24	, ⊢
	: , :
21	instantiation	25, 34, 35, 26	, , , ⊢
	: , : , :
22	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
23	instantiation	27, 34	⊢
	:
24	assumption		⊢
25	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
26	modus ponens	28, 29	, , , ⊢
27	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
28	instantiation	30, 40, 31, 32	, , ⊢
	: , : , : , : , : , :
29	assumption		⊢
30	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
31	instantiation	33, 34, 35	, ⊢
	: , :
32	instantiation	36, 37	⊢
	: , :
33	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
34	assumption		⊢
35	assumption		⊢
36	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
37	instantiation	38, 39, 40	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
40	assumption		⊢