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	, ⊢
	:
1	theorem		⊢
	proveit.numbers.negation.complex_closure
2	instantiation	3, 4, 5, 6	, ⊢
	: , :
3	theorem		⊢
	proveit.numbers.division.div_complex_closure
4	instantiation	18, 7, 8	, ⊢
	: , : , :
5	instantiation	69, 41, 9	⊢
	: , : , :
6	instantiation	10, 11	⊢
	:
7	instantiation	34, 21, 12	, ⊢
	: , :
8	instantiation	13, 14, 15	, ⊢
	: , : , :
9	instantiation	69, 47, 16	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
11	instantiation	17, 66, 63	⊢
	: , :
12	instantiation	18, 19, 20	, ⊢
	: , : , :
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	26, 71, 22, 27, 24, 28, 21, 35, 36, 30	, ⊢
	: , : , : , : , : , :
15	instantiation	26, 27, 66, 22, 28, 23, 24, 31, 32, 35, 36, 30	, ⊢
	: , : , : , : , : , :
16	instantiation	69, 50, 59	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
18	theorem		⊢
	proveit.logic.equality.sub_right_side_into
19	instantiation	34, 25, 30	, ⊢
	: , :
20	instantiation	26, 27, 66, 71, 28, 29, 35, 36, 30	, ⊢
	: , : , : , : , : , :
21	instantiation	34, 31, 32	⊢
	: , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
23	instantiation	37	⊢
	: , :
24	instantiation	33	⊢
	: , : , :
25	instantiation	34, 35, 36	⊢
	: , :
26	theorem		⊢
	proveit.numbers.multiplication.disassociation
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
29	instantiation	37	⊢
	: , :
30	instantiation	69, 41, 38	⊢
	: , : , :
31	instantiation	69, 41, 39	⊢
	: , : , :
32	instantiation	69, 41, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
34	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
36	instantiation	69, 41, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
38	instantiation	69, 47, 43	⊢
	: , : , :
39	instantiation	69, 47, 44	⊢
	: , : , :
40	instantiation	69, 45, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	69, 47, 48	⊢
	: , : , :
43	instantiation	69, 50, 49	⊢
	: , : , :
44	instantiation	69, 50, 62	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	69, 50, 51	⊢
	: , : , :
49	instantiation	69, 53, 52	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	69, 53, 54	⊢
	: , : , :
52	assumption		⊢
53	instantiation	55, 56, 57	⊢
	: , :
54	assumption		⊢
55	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
56	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
57	instantiation	58, 59, 60	⊢
	: , :
58	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
59	instantiation	61, 62, 63	⊢
	: , :
60	instantiation	64, 65	⊢
	:
61	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
62	instantiation	69, 70, 66	⊢
	: , : , :
63	instantiation	69, 67, 68	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	instantiation	69, 70, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
67	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
68	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat1