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, 62, 69, 9, 5, 11, 12, 58, 37	⊢
	: , : , : , : , : , :
3	instantiation	42, 6, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.disassociation
5	instantiation	15	⊢
	: , :
6	instantiation	8, 69, 9, 10, 11, 12, 58	⊢
	: , : , : , :
7	instantiation	18, 13, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	instantiation	15	⊢
	: , :
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	16, 37, 58, 17	⊢
	: , :
13	instantiation	18, 19, 20	⊢
	: , : , :
14	instantiation	21, 22, 23, 24	⊢
	: , : , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16	theorem		⊢
	proveit.numbers.division.div_complex_closure
17	instantiation	25, 56	⊢
	:
18	theorem		⊢
	proveit.logic.equality.sub_right_side_into
19	instantiation	26, 37, 27, 28	⊢
	: , : , : , : , :
20	instantiation	42, 29, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
22	instantiation	50, 31	⊢
	: , : , :
23	instantiation	50, 31	⊢
	: , : , :
24	instantiation	57, 37	⊢
	:
25	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
26	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
27	instantiation	67, 33, 32	⊢
	: , : , :
28	instantiation	67, 33, 34	⊢
	: , : , :
29	instantiation	50, 35	⊢
	: , : , :
30	instantiation	50, 36	⊢
	: , : , :
31	instantiation	52, 37	⊢
	:
32	instantiation	67, 39, 38	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
34	instantiation	67, 39, 40	⊢
	: , : , :
35	instantiation	50, 41	⊢
	: , : , :
36	instantiation	42, 43, 44	⊢
	: , : , :
37	instantiation	67, 60, 45	⊢
	: , : , :
38	instantiation	67, 47, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
40	instantiation	67, 47, 48	⊢
	: , : , :
41	instantiation	49, 58	⊢
	:
42	axiom		⊢
	proveit.logic.equality.equals_transitivity
43	instantiation	50, 51	⊢
	: , : , :
44	instantiation	52, 58	⊢
	:
45	instantiation	67, 63, 53	⊢
	: , : , :
46	instantiation	67, 55, 54	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
48	instantiation	67, 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	instantiation	67, 65, 59	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
57	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
58	instantiation	67, 60, 61	⊢
	: , : , :
59	instantiation	67, 68, 62	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
61	instantiation	67, 63, 64	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
64	instantiation	67, 65, 66	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	67, 68, 69	⊢
	: , : , :
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.nat2