logo

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, 3, 4, 5, 6*  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
2instantiation57, 36, 7  ⊢  
  : , : , :
3instantiation57, 40, 8  ⊢  
  : , : , :
4reference23  ⊢  
5instantiation9, 59  ⊢  
  :
6instantiation10, 11, 12  ⊢  
  : , : , :
7instantiation57, 40, 13  ⊢  
  : , : , :
8instantiation57, 47, 14  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
10axiom  ⊢  
 proveit.logic.equality.equals_transitivity
11instantiation15, 26, 31, 52, 28, 27, 29, 30, 16  ⊢  
  : , : , : , : , : , :
12instantiation17, 31, 26, 27, 28, 29, 30, 18, 19*  ⊢  
  : , : , : , : , :
13instantiation57, 39, 20  ⊢  
  : , : , :
14instantiation21, 48, 22  ⊢  
  : , :
15theorem  ⊢  
 proveit.numbers.multiplication.disassociation
16instantiation57, 36, 23  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_any
18instantiation57, 36, 24  ⊢  
  : , : , :
19instantiation25, 31, 26, 27, 28, 29, 30  ⊢  
  : , : , : , :
20instantiation57, 51, 31  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
22instantiation57, 58, 44  ⊢  
  : , : , :
23instantiation57, 40, 32  ⊢  
  : , : , :
24instantiation57, 40, 33  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
26axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
27instantiation34  ⊢  
  : , :
28theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
29instantiation57, 36, 35  ⊢  
  : , : , :
30instantiation57, 36, 37  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
32instantiation57, 39, 38  ⊢  
  : , : , :
33instantiation57, 39, 46  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
35instantiation57, 40, 41  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
37instantiation42, 43, 44  ⊢  
  : , : , :
38instantiation45, 46  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
41instantiation57, 47, 48  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
43instantiation49, 50  ⊢  
  : , :
44axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
45theorem  ⊢  
 proveit.numbers.negation.int_closure
46instantiation57, 51, 52  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
48instantiation53, 54, 55  ⊢  
  : , :
49theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
53theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
54instantiation57, 58, 56  ⊢  
  : , : , :
55instantiation57, 58, 59  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
59theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements