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
| step type | requirements | statement | ||
|---|---|---|---|---|
| 0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 | ⊢ ![]() | |
: , : , : , : , : , : ![]() | ||||
| 1 | theorem | ⊢ ![]() | ||
| proveit.numbers.addition.association | ||||
| 2 | reference | 38 | ⊢ ![]() | |
| 3 | reference | 37 | ⊢ ![]() | |
| 4 | instantiation | 13 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 5 | instantiation | 14 | ⊢ ![]() | |
: , : ![]() | ||||
| 6 | instantiation | 14 | ⊢ ![]() | |
: , : ![]() | ||||
| 7 | instantiation | 41, 20, 15 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 8 | instantiation | 41, 20, 16 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 9 | instantiation | 41, 20, 17 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 10 | instantiation | 41, 20, 18 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 11 | instantiation | 41, 20, 19 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 12 | instantiation | 41, 20, 21 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 13 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq | ||||
| 14 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq | ||||
| 15 | instantiation | 41, 27, 22 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 16 | instantiation | 41, 27, 23 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 17 | instantiation | 41, 27, 24 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 18 | instantiation | 41, 27, 25 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 19 | instantiation | 41, 27, 26 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 20 | theorem | ⊢ ![]() | ||
| proveit.numbers.number_sets.complex_numbers.real_within_complex | ||||
| 21 | instantiation | 41, 27, 28 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 22 | instantiation | 41, 34, 29 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 23 | instantiation | 41, 34, 30 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 24 | instantiation | 41, 34, 31 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 25 | instantiation | 41, 34, 32 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 26 | instantiation | 41, 34, 33 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 27 | theorem | ⊢ ![]() | ||
| proveit.numbers.number_sets.real_numbers.rational_within_real | ||||
| 28 | instantiation | 41, 34, 35 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 29 | instantiation | 41, 42, 36 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 30 | instantiation | 41, 42, 37 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 31 | instantiation | 41, 42, 38 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 32 | instantiation | 41, 42, 39 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 33 | instantiation | 41, 42, 40 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 34 | theorem | ⊢ ![]() | ||
| proveit.numbers.number_sets.rational_numbers.int_within_rational | ||||
| 35 | instantiation | 41, 42, 43 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 36 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.nat1 | ||||
| 37 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.nat2 | ||||
| 38 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.nat3 | ||||
| 39 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.nat4 | ||||
| 40 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.nat5 | ||||
| 41 | theorem | ⊢ ![]() | ||
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset | ||||
| 42 | theorem | ⊢ ![]() | ||
| proveit.numbers.number_sets.integers.nat_within_int | ||||
| 43 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.nat6 | ||||