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