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, 4, 5, 6, 7, 8, 9, 10, 11, 12^*	, , , ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.association
2	reference	60	⊢
3	instantiation	13	⊢
	: , :
4	instantiation	13	⊢
	: , :
5	instantiation	13	⊢
	: , :
6	instantiation	61, 46, 14	⊢
	: , : , :
7	instantiation	15, 16	⊢
	:
8	reference	36	⊢
9	instantiation	17, 36, 38, 18	⊢
	: , :
10	instantiation	19, 20, 36	⊢
	: , :
11	instantiation	61, 46, 21	⊢
	: , : , :
12	instantiation	22, 36, 23, 24, 25^, 26^, 27^*	⊢
	: , : , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	instantiation	61, 40, 28	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
16	instantiation	61, 46, 29	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.division.div_complex_closure
18	instantiation	30, 56	⊢
	:
19	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
20	instantiation	61, 46, 31	⊢
	: , : , :
21	assumption		⊢
22	theorem		⊢
	proveit.numbers.division.prod_of_fracs
23	instantiation	61, 33, 32	⊢
	: , : , :
24	instantiation	61, 33, 34	⊢
	: , : , :
25	instantiation	35, 36	⊢
	:
26	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
27	instantiation	37, 38	⊢
	:
28	assumption		⊢
29	instantiation	61, 40, 39	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
31	instantiation	61, 40, 41	⊢
	: , : , :
32	instantiation	61, 43, 42	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
34	instantiation	61, 43, 44	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.division.frac_one_denom
36	instantiation	61, 46, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
38	instantiation	61, 46, 47	⊢
	: , : , :
39	assumption		⊢
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
41	assumption		⊢
42	instantiation	61, 49, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
44	instantiation	61, 49, 50	⊢
	: , : , :
45	instantiation	61, 52, 51	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	61, 52, 53	⊢
	: , : , :
48	instantiation	61, 55, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
50	instantiation	61, 55, 56	⊢
	: , : , :
51	instantiation	61, 58, 57	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	61, 58, 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.posnat3
57	instantiation	61, 62, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
59	instantiation	61, 62, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
61	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements