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 | 9 | ⊢  | |
| 2 | instantiation | 9, 4, 5 | , , , , , , ⊢  | |
: , :  , : | ||||
| 3 | instantiation | 6, 47, 38, 7, 78, 70, 74, 15, 16, 8* | , , , , , , ⊢  | |
 :  ,  :  ,  :  ,  :  | ||||
| 4 | instantiation | 9, 10, 11 | , , , , , , ⊢  | |
: , :  , : | ||||
| 5 | instantiation | 20, 38, 78, 62, 15, 12 | , , , , , , ⊢  | |
: ,  : , :  , :  ,  : | ||||
| 6 | theorem | ⊢  | ||
| proveit.physics.quantum.algebra.qmult_scalar_association | ||||
| 7 | instantiation | 53 | ⊢  | |
 : , :  ,  :  | ||||
| 8 | instantiation | 13, 68, 14, 15, 16 | , , , , , , ⊢  | |
: , :  ,  : | ||||
| 9 | axiom | ⊢ | ||
| proveit.logic.equality.equals_transitivity | ||||
| 10 | instantiation | 20, 17, 37, 74, 18, 40, 19 | , , , , , , ⊢  | |
:  , :  , : , :  , :  | ||||
| 11 | instantiation | 20, 21, 39, 70, 48, 22 | , , , , , , ⊢  | |
: , :  , : , :  , :  | ||||
| 12 | instantiation | 58, 23, 24 | , , , , , ⊢  | |
 :  , :  , :  | ||||
| 13 | theorem | ⊢  | ||
| proveit.physics.quantum.algebra.scalar_mult_factorization | ||||
| 14 | instantiation | 25, 26, 27 | , , ⊢  | |
:  , :  , : | ||||
| 15 | instantiation | 76 | ⊢  | |
: , :  | ||||
| 16 | instantiation | 44, 79, 80, 81, 46 | , , , ⊢  | |
 :  ,  :  , : ,  : | ||||
| 17 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.nat4 | ||||
| 18 | instantiation | 28 | ⊢  | |
: , : , : ,  : | ||||
| 19 | instantiation | 58, 29, 30 | , , , , , ⊢  | |
: , :  , :  | ||||
| 20 | theorem | ⊢  | ||
| proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front | ||||
| 21 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.nat3 | ||||
| 22 | instantiation | 58, 31, 32 | , , , , , ⊢  | |
: , :  , :  | ||||
| 23 | instantiation | 44, 79, 80, 33, 46 | , , , , , ⊢  | |
: , : , :  , : | ||||
| 24 | instantiation | 67, 47, 34 | ⊢  | |
 : , :  , : | ||||
| 25 | theorem | ⊢  | ||
| proveit.logic.equality.sub_right_side_into | ||||
| 26 | instantiation | 50, 35, 74 | , , ⊢  | |
:  , : | ||||
| 27 | instantiation | 36, 37, 38, 39, 40, 41, 78, 70, 74 | , , ⊢  | |
 : , : ,  : , : , :  , :  | ||||
| 28 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.tuple_len_4_typical_eq | ||||
| 29 | instantiation | 44, 79, 80, 42, 46 | , , , , , ⊢  | |
: , : , :  , : | ||||
| 30 | instantiation | 67, 47, 43 | ⊢  | |
: , :  , : | ||||
| 31 | instantiation | 44, 79, 80, 45, 46 | , , , , , ⊢  | |
: , : , :  , : | ||||
| 32 | instantiation | 67, 47, 48 | ⊢  | |
| : , : , : | ||||
| 33 | instantiation | 71, 79, 80, 49 | , , , , ⊢  | |
| : , : , : | ||||
| 34 | instantiation | 53 | ⊢  | |
| : , : , : | ||||
| 35 | instantiation | 50, 78, 70 | , ⊢  | |
| : , : | ||||
| 36 | theorem | ⊢  | ||
| proveit.numbers.multiplication.disassociation | ||||
| 37 | axiom | ⊢  | ||
| proveit.numbers.number_sets.natural_numbers.zero_in_nats | ||||
| 38 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.nat2 | ||||
| 39 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.nat1 | ||||
| 40 | theorem | ⊢  | ||
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq | ||||
| 41 | instantiation | 76 | ⊢  | |
| : , : | ||||
| 42 | instantiation | 71, 79, 80, 51 | , , , , ⊢  | |
| : , : , : | ||||
| 43 | instantiation | 53 | ⊢  | |
| : , : , : | ||||
| 44 | theorem | ⊢  | ||
| proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain | ||||
| 45 | instantiation | 71, 79, 80, 52 | , , , , ⊢  | |
| : , : , : | ||||
| 46 | assumption | ⊢ | ||
| 47 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.posnat3 | ||||
| 48 | instantiation | 53 | ⊢  | |
| : , : , : | ||||
| 49 | instantiation | 58, 54, 55 | , , , , ⊢  | |
:  , : , :  | ||||
| 50 | theorem | ⊢  | ||
| proveit.numbers.multiplication.mult_complex_closure_bin | ||||
| 51 | instantiation | 58, 56, 57 | , , , , ⊢  | |
: , : , :  | ||||
| 52 | instantiation | 58, 59, 60 | , , , , ⊢  | |
: , : , :  | ||||
| 53 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq | ||||
| 54 | instantiation | 77, 61, 79, 80, 81 | , , , , ⊢  | |
:  , : , : , : | ||||
| 55 | instantiation | 67, 68, 62 | ⊢  | |
| : , : , : | ||||
| 56 | instantiation | 63, 70, 79, 80, 64 | , , , , ⊢  | |
: , : , : , :  | ||||
| 57 | instantiation | 67, 68, 65 | ⊢  | |
: , :  , : | ||||
| 58 | theorem | ⊢  | ||
| proveit.logic.equality.sub_left_side_into | ||||
| 59 | instantiation | 77, 66, 79, 80, 81 | , , , , ⊢  | |
:  , : , : , : | ||||
| 60 | instantiation | 67, 68, 69 | ⊢  | |
: , :  , : | ||||
| 61 | instantiation | 73, 70, 75, 74 | , ⊢  | |
: , :  , : | ||||
| 62 | instantiation | 76 | ⊢  | |
| : , : | ||||
| 63 | theorem | ⊢  | ||
| proveit.physics.quantum.algebra.qmult_op_complex_closure | ||||
| 64 | instantiation | 71, 79, 80, 72 | , , , ⊢  | |
| : , : , : | ||||
| 65 | instantiation | 76 | ⊢  | |
| : , : | ||||
| 66 | instantiation | 73, 74, 75, 78 | , ⊢  | |
| : , : , : | ||||
| 67 | axiom | ⊢  | ||
| proveit.physics.quantum.algebra.multi_qmult_def | ||||
| 68 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.posnat2 | ||||
| 69 | instantiation | 76 | ⊢  | |
| : , : | ||||
| 70 | assumption | ⊢ | ||
| 71 | theorem | ⊢  | ||
| proveit.physics.quantum.algebra.qmult_op_is_linmap | ||||
| 72 | instantiation | 77, 78, 79, 80, 81 | , , , ⊢  | |
| : , : , : , : | ||||
| 73 | theorem | ⊢  | ||
| proveit.physics.quantum.algebra.qmult_complex_ket_closure | ||||
| 74 | assumption | ⊢ | ||
| 75 | theorem | ⊢  | ||
| proveit.linear_algebra.inner_products.complex_set_is_hilbert_space | ||||
| 76 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq | ||||
| 77 | theorem | ⊢  | ||
| proveit.physics.quantum.algebra.qmult_complex_op_closure | ||||
| 78 | assumption | ⊢ | ||
| 79 | instantiation | 82, 85 | ⊢  | |
| : | ||||
| 80 | instantiation | 82, 84 | ⊢  | |
| : | ||||
| 81 | instantiation | 83, 84, 85, 86 | , , ⊢  | |
: , : ,  : | ||||
| 82 | theorem | ⊢  | ||
| proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space | ||||
| 83 | theorem | ⊢  | ||
| proveit.physics.quantum.algebra.qmult_matrix_is_linmap | ||||
| 84 | assumption | ⊢ | ||
| 85 | assumption | ⊢ | ||
| 86 | assumption | ⊢ | ||
| *equality replacement requirements | ||||