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