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	46	⊢
2	instantiation	4, 9, 10, 11, 5, 62, 14, 13	, , , ⊢
	: , : , : , : , : , : , :
3	instantiation	46, 6, 7	, , , ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	instantiation	16	⊢
	: , :
6	instantiation	8, 9, 10, 69, 11, 12, 13, 62, 14	, , , ⊢
	: , : , : , : , : , :
7	instantiation	54, 15	, , ⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.association
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	16	⊢
	: , :
13	instantiation	17, 41, 62, 38	, , ⊢
	: , :
14	instantiation	67, 65, 18	⊢
	: , : , :
15	instantiation	21, 19, 20	, , ⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17	theorem		⊢
	proveit.numbers.division.div_complex_closure
18	assumption		⊢
19	instantiation	21, 22, 23	, , ⊢
	: , : , :
20	instantiation	24, 25, 26, 27	⊢
	: , : , : , :
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	28, 41, 42, 29, 30	, , ⊢
	: , : , : , : , :
23	instantiation	46, 31, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
25	instantiation	54, 33	⊢
	: , : , :
26	instantiation	54, 34	⊢
	: , : , :
27	instantiation	61, 41	⊢
	:
28	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
29	instantiation	67, 35, 36	⊢
	: , : , :
30	instantiation	37, 62, 38	, ⊢
	:
31	instantiation	54, 39	⊢
	: , : , :
32	instantiation	54, 40	⊢
	: , : , :
33	instantiation	56, 41	⊢
	:
34	instantiation	56, 42	⊢
	:
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
36	instantiation	67, 43, 44	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
38	assumption		⊢
39	instantiation	54, 45	⊢
	: , : , :
40	instantiation	46, 47, 48	⊢
	: , : , :
41	instantiation	67, 65, 49	⊢
	: , : , :
42	instantiation	67, 65, 50	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
44	instantiation	67, 51, 52	⊢
	: , : , :
45	instantiation	53, 62	⊢
	:
46	axiom		⊢
	proveit.logic.equality.equals_transitivity
47	instantiation	54, 55	⊢
	: , : , :
48	instantiation	56, 62	⊢
	:
49	assumption		⊢
50	instantiation	67, 57, 58	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
52	instantiation	67, 59, 60	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
54	axiom		⊢
	proveit.logic.equality.substitution
55	instantiation	61, 62	⊢
	:
56	theorem		⊢
	proveit.numbers.division.frac_one_denom
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
58	instantiation	67, 63, 64	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
61	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
62	instantiation	67, 65, 66	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
64	instantiation	67, 68, 69	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
66	assumption		⊢
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