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	reference	42	⊢
2	instantiation	4, 5, 6, 65, 7, 8, 9, 58, 10	, , , ⊢
	: , : , : , : , : , :
3	instantiation	50, 11	, , ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.association
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	12	⊢
	: , :
9	instantiation	13, 37, 58, 34	, , ⊢
	: , :
10	instantiation	63, 61, 14	⊢
	: , : , :
11	instantiation	17, 15, 16	, , ⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	theorem		⊢
	proveit.numbers.division.div_complex_closure
14	assumption		⊢
15	instantiation	17, 18, 19	, , ⊢
	: , : , :
16	instantiation	20, 21, 22, 23	⊢
	: , : , : , :
17	theorem		⊢
	proveit.logic.equality.sub_right_side_into
18	instantiation	24, 37, 38, 25, 26	, , ⊢
	: , : , : , : , :
19	instantiation	42, 27, 28	⊢
	: , : , :
20	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
21	instantiation	50, 29	⊢
	: , : , :
22	instantiation	50, 30	⊢
	: , : , :
23	instantiation	57, 37	⊢
	:
24	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
25	instantiation	63, 31, 32	⊢
	: , : , :
26	instantiation	33, 58, 34	, ⊢
	:
27	instantiation	50, 35	⊢
	: , : , :
28	instantiation	50, 36	⊢
	: , : , :
29	instantiation	52, 37	⊢
	:
30	instantiation	52, 38	⊢
	:
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
32	instantiation	63, 39, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
34	assumption		⊢
35	instantiation	50, 41	⊢
	: , : , :
36	instantiation	42, 43, 44	⊢
	: , : , :
37	instantiation	63, 61, 45	⊢
	: , : , :
38	instantiation	63, 61, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
40	instantiation	63, 47, 48	⊢
	: , : , :
41	instantiation	49, 58	⊢
	:
42	axiom		⊢
	proveit.logic.equality.equals_transitivity
43	instantiation	50, 51	⊢
	: , : , :
44	instantiation	52, 58	⊢
	:
45	assumption		⊢
46	instantiation	63, 53, 54	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
48	instantiation	63, 55, 56	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
50	axiom		⊢
	proveit.logic.equality.substitution
51	instantiation	57, 58	⊢
	:
52	theorem		⊢
	proveit.numbers.division.frac_one_denom
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
54	instantiation	63, 59, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
57	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
58	instantiation	63, 61, 62	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
60	instantiation	63, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
62	assumption		⊢
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat1