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	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	32, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	8, 9, 17, 10, 11, 12	⊢
	: , : , : , : , :
6	instantiation	13, 14, 15	⊢
	: , : , :
7	instantiation	16, 17	⊢
	:
8	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
9	instantiation	56, 49, 18	⊢
	: , : , :
10	instantiation	56, 21, 19	⊢
	: , : , :
11	instantiation	56, 21, 20	⊢
	: , : , :
12	instantiation	56, 21, 22	⊢
	: , : , :
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	32, 23	⊢
	: , : , :
15	instantiation	32, 24	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.division.frac_one_denom
17	instantiation	56, 49, 25	⊢
	: , : , :
18	instantiation	56, 52, 26	⊢
	: , : , :
19	instantiation	56, 29, 27	⊢
	: , : , :
20	instantiation	56, 29, 28	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
22	instantiation	56, 29, 30	⊢
	: , : , :
23	instantiation	32, 31	⊢
	: , : , :
24	instantiation	32, 33	⊢
	: , : , :
25	instantiation	56, 52, 34	⊢
	: , : , :
26	instantiation	56, 54, 35	⊢
	: , : , :
27	instantiation	56, 38, 36	⊢
	: , : , :
28	instantiation	56, 38, 37	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
30	instantiation	56, 38, 39	⊢
	: , : , :
31	instantiation	40, 42	⊢
	:
32	axiom		⊢
	proveit.logic.equality.substitution
33	instantiation	41, 42	⊢
	:
34	instantiation	56, 54, 43	⊢
	: , : , :
35	instantiation	56, 57, 44	⊢
	: , : , :
36	instantiation	56, 47, 45	⊢
	: , : , :
37	instantiation	56, 47, 46	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
39	instantiation	56, 47, 48	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
41	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
42	instantiation	56, 49, 50	⊢
	: , : , :
43	instantiation	56, 57, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	56, 52, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	56, 54, 55	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
55	instantiation	56, 57, 58	⊢
	: , : , :
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat2