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	38	⊢
2	instantiation	4, 65, 5, 6, 7, 8, 54	⊢
	: , : , : , :
3	instantiation	14, 9, 10	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	instantiation	11	⊢
	: , :
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	12, 33, 54, 13	⊢
	: , :
9	instantiation	14, 15, 16	⊢
	: , : , :
10	instantiation	17, 18, 19, 20	⊢
	: , : , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12	theorem		⊢
	proveit.numbers.division.div_complex_closure
13	instantiation	21, 52	⊢
	:
14	theorem		⊢
	proveit.logic.equality.sub_right_side_into
15	instantiation	22, 33, 23, 24	⊢
	: , : , : , : , :
16	instantiation	38, 25, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
18	instantiation	46, 27	⊢
	: , : , :
19	instantiation	46, 27	⊢
	: , : , :
20	instantiation	53, 33	⊢
	:
21	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
22	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
23	instantiation	63, 29, 28	⊢
	: , : , :
24	instantiation	63, 29, 30	⊢
	: , : , :
25	instantiation	46, 31	⊢
	: , : , :
26	instantiation	46, 32	⊢
	: , : , :
27	instantiation	48, 33	⊢
	:
28	instantiation	63, 35, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
30	instantiation	63, 35, 36	⊢
	: , : , :
31	instantiation	46, 37	⊢
	: , : , :
32	instantiation	38, 39, 40	⊢
	: , : , :
33	instantiation	63, 56, 41	⊢
	: , : , :
34	instantiation	63, 43, 42	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
36	instantiation	63, 43, 44	⊢
	: , : , :
37	instantiation	45, 54	⊢
	:
38	axiom		⊢
	proveit.logic.equality.equals_transitivity
39	instantiation	46, 47	⊢
	: , : , :
40	instantiation	48, 54	⊢
	:
41	instantiation	63, 59, 49	⊢
	: , : , :
42	instantiation	63, 51, 50	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
44	instantiation	63, 51, 52	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
46	axiom		⊢
	proveit.logic.equality.substitution
47	instantiation	53, 54	⊢
	:
48	theorem		⊢
	proveit.numbers.division.frac_one_denom
49	instantiation	63, 61, 55	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
53	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
54	instantiation	63, 56, 57	⊢
	: , : , :
55	instantiation	63, 64, 58	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	instantiation	63, 59, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	63, 61, 62	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	63, 64, 65	⊢
	: , : , :
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.nat2