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 | , , , , ⊢ ![]() | |
: , : , : ![]() | ||||
| 1 | reference | 8 | ⊢ ![]() | |
| 2 | instantiation | 49, 43, 4 | , , , , ⊢ ![]() | |
: , : ![]() | ||||
| 3 | instantiation | 5, 6, 7 | , , , , ⊢ ![]() | |
: , : , : ![]() | ||||
| 4 | instantiation | 8, 9, 10 | , , ⊢ ![]() | |
: , : , : ![]() | ||||
| 5 | axiom | ⊢ ![]() | ||
| proveit.logic.equality.equals_transitivity | ||||
| 6 | instantiation | 18, 21, 12, 19, 14, 22, 11, 24, 25, 26 | , , , , ⊢ ![]() | |
: , : , : , : , : , : ![]() | ||||
| 7 | instantiation | 18, 19, 20, 12, 22, 13, 14, 15, 16, 24, 25, 26 | , , , , ⊢ ![]() | |
: , : , : , : , : , : ![]() | ||||
| 8 | theorem | ⊢ ![]() | ||
| proveit.logic.equality.sub_right_side_into | ||||
| 9 | instantiation | 49, 17, 48 | , , ⊢ ![]() | |
: , : ![]() | ||||
| 10 | instantiation | 18, 19, 20, 21, 22, 23, 24, 25, 26 | , , ⊢ ![]() | |
: , : , : , : , : , : ![]() | ||||
| 11 | instantiation | 46, 34, 27 | , ⊢ ![]() | |
: , : , : ![]() | ||||
| 12 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.nat3 | ||||
| 13 | instantiation | 31 | ⊢ ![]() | |
: , : ![]() | ||||
| 14 | instantiation | 28 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 15 | instantiation | 46, 34, 29 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 16 | instantiation | 46, 34, 30 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 17 | instantiation | 49, 44, 45 | , ⊢ ![]() | |
: , : ![]() | ||||
| 18 | theorem | ⊢ ![]() | ||
| proveit.numbers.multiplication.disassociation | ||||
| 19 | axiom | ⊢ ![]() | ||
| proveit.numbers.number_sets.natural_numbers.zero_in_nats | ||||
| 20 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.nat2 | ||||
| 21 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.nat1 | ||||
| 22 | theorem | ⊢ ![]() | ||
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq | ||||
| 23 | instantiation | 31 | ⊢ ![]() | |
: , : ![]() | ||||
| 24 | instantiation | 46, 34, 32 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 25 | instantiation | 46, 34, 33 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 26 | instantiation | 46, 34, 35 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 27 | instantiation | 46, 41, 36 | , ⊢ ![]() | |
: , : , : ![]() | ||||
| 28 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.tuple_len_3_typical_eq | ||||
| 29 | instantiation | 46, 41, 37 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 30 | instantiation | 46, 41, 38 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 31 | theorem | ⊢ ![]() | ||
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq | ||||
| 32 | instantiation | 46, 41, 39 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 33 | instantiation | 46, 41, 40 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 34 | theorem | ⊢ ![]() | ||
| proveit.numbers.number_sets.complex_numbers.real_within_complex | ||||
| 35 | instantiation | 46, 41, 42 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 36 | instantiation | 46, 47, 43 | , ⊢ ![]() | |
: , : , : ![]() | ||||
| 37 | instantiation | 46, 47, 50 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 38 | instantiation | 46, 47, 51 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 39 | instantiation | 46, 47, 44 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 40 | instantiation | 46, 47, 45 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 41 | theorem | ⊢ ![]() | ||
| proveit.numbers.number_sets.real_numbers.rational_within_real | ||||
| 42 | instantiation | 46, 47, 48 | ⊢ ![]() | |
: , : , : ![]() | ||||
| 43 | instantiation | 49, 50, 51 | , ⊢ ![]() | |
: , : ![]() | ||||
| 44 | assumption | ⊢ ![]() | ||
| 45 | assumption | ⊢ ![]() | ||
| 46 | theorem | ⊢ ![]() | ||
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset | ||||
| 47 | theorem | ⊢ ![]() | ||
| proveit.numbers.number_sets.rational_numbers.int_within_rational | ||||
| 48 | assumption | ⊢ ![]() | ||
| 49 | theorem | ⊢ ![]() | ||
| proveit.numbers.multiplication.mult_int_closure_bin | ||||
| 50 | assumption | ⊢ ![]() | ||
| 51 | assumption | ⊢ ![]() | ||