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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 typerequirementsstatement
0instantiation1, 2  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.substitution
2instantiation3, 4, 5, 24, 6, 7*  ⊢  
  : , : , :
3theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
4instantiation58, 37, 8  ⊢  
  : , : , :
5instantiation58, 41, 9  ⊢  
  : , : , :
6instantiation10, 60  ⊢  
  :
7instantiation11, 12, 13  ⊢  
  : , : , :
8instantiation58, 41, 14  ⊢  
  : , : , :
9instantiation58, 48, 15  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
11axiom  ⊢  
 proveit.logic.equality.equals_transitivity
12instantiation16, 27, 32, 53, 29, 28, 30, 31, 17  ⊢  
  : , : , : , : , : , :
13instantiation18, 32, 27, 28, 29, 30, 31, 19, 20*  ⊢  
  : , : , : , : , :
14instantiation58, 40, 21  ⊢  
  : , : , :
15instantiation22, 49, 23  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.multiplication.disassociation
17instantiation58, 37, 24  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_any
19instantiation58, 37, 25  ⊢  
  : , : , :
20instantiation26, 32, 27, 28, 29, 30, 31  ⊢  
  : , : , : , :
21instantiation58, 52, 32  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
23instantiation58, 59, 45  ⊢  
  : , : , :
24instantiation58, 41, 33  ⊢  
  : , : , :
25instantiation58, 41, 34  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
27axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
28instantiation35  ⊢  
  : , :
29theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30instantiation58, 37, 36  ⊢  
  : , : , :
31instantiation58, 37, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
33instantiation58, 40, 39  ⊢  
  : , : , :
34instantiation58, 40, 47  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36instantiation58, 41, 42  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
38instantiation43, 44, 45  ⊢  
  : , : , :
39instantiation46, 47  ⊢  
  :
40theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
42instantiation58, 48, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
44instantiation50, 51  ⊢  
  : , :
45axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
46theorem  ⊢  
 proveit.numbers.negation.int_closure
47instantiation58, 52, 53  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
49instantiation54, 55, 56  ⊢  
  : , :
50theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
54theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
55instantiation58, 59, 57  ⊢  
  : , : , :
56instantiation58, 59, 60  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
58theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
60theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements