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