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 | modus ponens | 1, 2 |  ,  ,  ,  ,  ,  ,  ⊢  | |
| 1 | instantiation | 7, 20, 19, 22, 21, 23, 3, 4, 27, 26, 28, 29 | , , , ⊢  | |
 :  ,  :  ,  :  ,  :  ,  :  ,  :  ,  :  ,  : ,  :  ,  : ,  :  | ||||
| 2 | modus ponens | 5, 6 | , , , , , , ⊢  | |
| 3 | instantiation | 34 | ⊢  | |
:  , :  | ||||
| 4 | instantiation | 34 | ⊢  | |
: , :  | ||||
| 5 | instantiation | 7, 19, 10, 21, 23, 26, 28, 27, 13*, 14* | , , ⊢  | |
: , : , :  , : , : , :  , : , :  , : , :  , : | ||||
| 6 | modus ponens | 8, 9 | , , , , , , ⊢  | |
| 7 | theorem | ⊢  | ||
| proveit.linear_algebra.tensors.insert_vec_on_both_sides_of_equality | ||||
| 8 | instantiation | 18, 10, 19, 21, 23, 26, 28, 27, 11, 12, 13*, 14* | , , , ⊢  | |
: , : , : , : , : , : , : , : , : ,  : , : , : | ||||
| 9 | modus ponens | 15, 16 | , , , , , ⊢  | |
| 10 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.nat1 | ||||
| 11 | instantiation | 35 | ⊢  | |
| : | ||||
| 12 | assumption | ⊢ | ||
| 13 | instantiation | 17, 23, 26 | ⊢  | |
: , : ,  : | ||||
| 14 | instantiation | 17, 23, 28 | ⊢  | |
| : , : , : | ||||
| 15 | instantiation | 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 | , , , , ⊢  | |
: , : , : , : , : , : , : , :  , : , :  , : , : | ||||
| 16 | assumption | ⊢ | ||
| 17 | axiom | ⊢  | ||
| proveit.linear_algebra.tensors.unary_tensor_prod_def | ||||
| 18 | theorem | ⊢  | ||
| proveit.linear_algebra.tensors.remove_vec_on_both_sides_of_equality | ||||
| 19 | axiom | ⊢  | ||
| proveit.numbers.number_sets.natural_numbers.zero_in_nats | ||||
| 20 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.nat2 | ||||
| 21 | theorem | ⊢  | ||
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq | ||||
| 22 | instantiation | 34 | ⊢  | |
| : , : | ||||
| 23 | instantiation | 32, 33 | ⊢  | |
 :  | ||||
| 24 | instantiation | 34 | ⊢  | |
| : , : | ||||
| 25 | instantiation | 34 | ⊢  | |
| : , : | ||||
| 26 | assumption | ⊢ | ||
| 27 | assumption | ⊢ | ||
| 28 | assumption | ⊢ | ||
| 29 | assumption | ⊢ | ||
| 30 | instantiation | 35 | ⊢  | |
| : | ||||
| 31 | assumption | ⊢ | ||
| 32 | theorem | ⊢  | ||
| proveit.linear_algebra.real_vec_set_is_vec_space | ||||
| 33 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.posnat3 | ||||
| 34 | theorem | ⊢  | ||
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq | ||||
| 35 | axiom | ⊢  | ||
| proveit.logic.equality.equals_reflexivity | ||||
| *equality replacement requirements | ||||