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*  ⊢  
  : , :
1theorem  ⊢  
 proveit.logic.equality.equals_reversal
2instantiation4, 5, 77, 67, 6, 7, 8, 12, 9*  ⊢  
  : , : , : , : , : , :
3theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
4theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
5axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
6theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7instantiation10  ⊢  
  : , :
8instantiation75, 13, 20  ⊢  
  : , : , :
9instantiation11, 12  ⊢  
  :
10theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
12instantiation75, 13, 14  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
14modus ponens15, 16  ⊢  
15instantiation17  ⊢  
  : , : , :
16generalization18  ⊢  
17theorem  ⊢  
 proveit.numbers.summation.summation_real_closure
18instantiation19, 20, 21, 22,  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.division.div_real_closure
20instantiation75, 29, 23  ⊢  
  : , : , :
21instantiation24, 25, 77,  ⊢  
  : , :
22instantiation26, 27, 28,  ⊢  
  : , :
23instantiation75, 34, 64  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
25instantiation75, 29, 30,  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
27instantiation75, 32, 31,  ⊢  
  : , : , :
28instantiation75, 32, 33  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
30instantiation75, 34, 38,  ⊢  
  : , : , :
31instantiation75, 36, 35,  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
33instantiation75, 36, 37  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
35instantiation51, 38, 39,  ⊢  
  :
36theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
37theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
38instantiation75, 40, 47,  ⊢  
  : , : , :
39instantiation57, 41, 42,  ⊢  
  : , : , :
40instantiation62, 45, 46  ⊢  
  : , :
41instantiation43, 44  ⊢  
  :
42instantiation63, 45, 46, 47,  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
44instantiation48, 49, 61  ⊢  
  : , :
45instantiation68, 52, 64  ⊢  
  : , :
46instantiation68, 69, 50  ⊢  
  : , :
47assumption  ⊢  
48theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
49instantiation51, 52, 53  ⊢  
  :
50instantiation75, 54, 55  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
52instantiation75, 56, 66  ⊢  
  : , : , :
53instantiation57, 58, 59  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
55instantiation60, 61  ⊢  
  :
56instantiation62, 64, 65  ⊢  
  : , :
57theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
58theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
59instantiation63, 64, 65, 66  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
61theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
62theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
63theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
64instantiation75, 76, 67  ⊢  
  : , : , :
65instantiation68, 69, 70  ⊢  
  : , :
66assumption  ⊢  
67theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
68theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
69instantiation75, 71, 72  ⊢  
  : , : , :
70instantiation73, 74  ⊢  
  :
71theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
72theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
73theorem  ⊢  
 proveit.numbers.negation.int_closure
74instantiation75, 76, 77  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
77theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements