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