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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	5, 6, 49, 4, 8, 10, 11, 9, 12	, , , ⊢
	: , : , : , : , : , : , :
3	instantiation	5, 49, 6, 7, 8, 9, 10, 11, 12	, , , ⊢
	: , : , : , : , : , : , :
4	instantiation	13	⊢
	: , :
5	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
7	instantiation	13	⊢
	: , :
8	instantiation	14, 15, 16, 17	⊢
	: , :
9	instantiation	47, 32, 18	⊢
	: , : , :
10	instantiation	19, 20, 21	⊢
	: , :
11	instantiation	22, 23	⊢
	:
12	instantiation	47, 32, 24	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	theorem		⊢
	proveit.numbers.division.div_complex_closure
15	instantiation	47, 32, 25	⊢
	: , : , :
16	instantiation	47, 32, 26	⊢
	: , : , :
17	instantiation	27, 28	⊢
	:
18	instantiation	47, 39, 29	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
20	instantiation	47, 32, 30	⊢
	: , : , :
21	instantiation	47, 32, 31	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
23	instantiation	47, 32, 33	⊢
	: , : , :
24	assumption		⊢
25	instantiation	47, 37, 34	⊢
	: , : , :
26	instantiation	47, 37, 35	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
29	assumption		⊢
30	instantiation	47, 39, 36	⊢
	: , : , :
31	instantiation	47, 37, 38	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	47, 39, 40	⊢
	: , : , :
34	instantiation	47, 43, 41	⊢
	: , : , :
35	instantiation	47, 43, 42	⊢
	: , : , :
36	assumption		⊢
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	47, 43, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
40	assumption		⊢
41	instantiation	47, 48, 45	⊢
	: , : , :
42	instantiation	47, 48, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	instantiation	47, 48, 49	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat2