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 type	requirements	statement
0	instantiation	1, 2, 3, 4	, ⊢
	: , :
1	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
2	instantiation	16, 5, 6	, ⊢
	: , : , :
3	instantiation	67, 39, 7	⊢
	: , : , :
4	instantiation	8, 9	⊢
	:
5	instantiation	32, 19, 10	, ⊢
	: , :
6	instantiation	11, 12, 13	, ⊢
	: , : , :
7	instantiation	67, 45, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
9	instantiation	15, 64, 61	⊢
	: , :
10	instantiation	16, 17, 18	, ⊢
	: , : , :
11	axiom		⊢
	proveit.logic.equality.equals_transitivity
12	instantiation	24, 69, 20, 25, 22, 26, 19, 33, 34, 28	, ⊢
	: , : , : , : , : , :
13	instantiation	24, 25, 64, 20, 26, 21, 22, 29, 30, 33, 34, 28	, ⊢
	: , : , : , : , : , :
14	instantiation	67, 48, 57	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
16	theorem		⊢
	proveit.logic.equality.sub_right_side_into
17	instantiation	32, 23, 28	, ⊢
	: , :
18	instantiation	24, 25, 64, 69, 26, 27, 33, 34, 28	, ⊢
	: , : , : , : , : , :
19	instantiation	32, 29, 30	⊢
	: , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
21	instantiation	35	⊢
	: , :
22	instantiation	31	⊢
	: , : , :
23	instantiation	32, 33, 34	⊢
	: , :
24	theorem		⊢
	proveit.numbers.multiplication.disassociation
25	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	35	⊢
	: , :
28	instantiation	67, 39, 36	⊢
	: , : , :
29	instantiation	67, 39, 37	⊢
	: , : , :
30	instantiation	67, 39, 38	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
32	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
34	instantiation	67, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	instantiation	67, 45, 41	⊢
	: , : , :
37	instantiation	67, 45, 42	⊢
	: , : , :
38	instantiation	67, 43, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	instantiation	67, 45, 46	⊢
	: , : , :
41	instantiation	67, 48, 47	⊢
	: , : , :
42	instantiation	67, 48, 60	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	67, 48, 49	⊢
	: , : , :
47	instantiation	67, 51, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	instantiation	67, 51, 52	⊢
	: , : , :
50	assumption		⊢
51	instantiation	53, 54, 55	⊢
	: , :
52	assumption		⊢
53	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
54	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
55	instantiation	56, 57, 58	⊢
	: , :
56	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
57	instantiation	59, 60, 61	⊢
	: , :
58	instantiation	62, 63	⊢
	:
59	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
60	instantiation	67, 68, 64	⊢
	: , : , :
61	instantiation	67, 65, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.negation.int_closure
63	instantiation	67, 68, 69	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
65	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
66	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat1