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