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	⊢
	: , : , :
1	reference	33	⊢
2	instantiation	5, 3, 4	⊢
	: , : , :
3	instantiation	5, 6, 7	⊢
	: , : , :
4	instantiation	33, 8	⊢
	: , : , :
5	theorem		⊢
	proveit.logic.equality.sub_right_side_into
6	instantiation	9, 10, 18, 11, 12, 13	⊢
	: , : , : , : , :
7	instantiation	14, 15, 16	⊢
	: , : , :
8	instantiation	17, 18	⊢
	:
9	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
10	instantiation	57, 50, 19	⊢
	: , : , :
11	instantiation	57, 22, 20	⊢
	: , : , :
12	instantiation	57, 22, 21	⊢
	: , : , :
13	instantiation	57, 22, 23	⊢
	: , : , :
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	33, 24	⊢
	: , : , :
16	instantiation	33, 25	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.division.frac_one_denom
18	instantiation	57, 50, 26	⊢
	: , : , :
19	instantiation	57, 53, 27	⊢
	: , : , :
20	instantiation	57, 30, 28	⊢
	: , : , :
21	instantiation	57, 30, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
23	instantiation	57, 30, 31	⊢
	: , : , :
24	instantiation	33, 32	⊢
	: , : , :
25	instantiation	33, 34	⊢
	: , : , :
26	instantiation	57, 53, 35	⊢
	: , : , :
27	instantiation	57, 55, 36	⊢
	: , : , :
28	instantiation	57, 39, 37	⊢
	: , : , :
29	instantiation	57, 39, 38	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31	instantiation	57, 39, 40	⊢
	: , : , :
32	instantiation	41, 43	⊢
	:
33	axiom		⊢
	proveit.logic.equality.substitution
34	instantiation	42, 43	⊢
	:
35	instantiation	57, 55, 44	⊢
	: , : , :
36	instantiation	57, 58, 45	⊢
	: , : , :
37	instantiation	57, 48, 46	⊢
	: , : , :
38	instantiation	57, 48, 47	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
40	instantiation	57, 48, 49	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
42	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
43	instantiation	57, 50, 51	⊢
	: , : , :
44	instantiation	57, 58, 52	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
51	instantiation	57, 53, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
54	instantiation	57, 55, 56	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	57, 58, 59	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat3