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^*	, ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
2	instantiation	55, 35, 8	⊢
	: , : , :
3	assumption		⊢
4	instantiation	9, 10	⊢
	:
5	instantiation	11, 12	⊢
	:
6	assumption		⊢
7	instantiation	13, 14, 15, 16, 17^, 18^	⊢
	: , : , :
8	instantiation	55, 45, 19	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.negation.real_closure
10	instantiation	55, 45, 20	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_if_in_rational_nonzero
12	instantiation	55, 21, 29	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.exponentiation.neg_power_of_quotient
14	instantiation	55, 23, 22	⊢
	: , : , :
15	instantiation	55, 23, 24	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
17	instantiation	26, 25	⊢
	:
18	instantiation	26, 27	⊢
	:
19	instantiation	55, 28, 29	⊢
	: , : , :
20	instantiation	55, 52, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
22	instantiation	55, 32, 31	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
24	instantiation	55, 32, 33	⊢
	: , : , :
25	instantiation	55, 35, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
27	instantiation	55, 35, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
29	instantiation	37, 38, 39	⊢
	: , :
30	instantiation	55, 56, 40	⊢
	: , : , :
31	instantiation	55, 42, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
33	instantiation	55, 42, 43	⊢
	: , : , :
34	instantiation	55, 45, 44	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
36	instantiation	55, 45, 46	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
38	instantiation	55, 47, 48	⊢
	: , : , :
39	instantiation	55, 47, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
41	instantiation	55, 49, 48	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
43	instantiation	55, 49, 50	⊢
	: , : , :
44	instantiation	55, 52, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	55, 52, 53	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
51	instantiation	55, 56, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	instantiation	55, 56, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements