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