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 | ⊢ |