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	11, 4	, , , , ⊢
	: , :
3	instantiation	5, 6, 7	, , , , ⊢
	: , : , :
4	instantiation	8, 22, 23, 25	, , , , ⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.equals_transitivity
6	instantiation	9, 10	, ⊢
	: , : , :
7	instantiation	11, 12	, , , , ⊢
	: , :
8	theorem		⊢
	proveit.numbers.division.frac_cancel_left
9	axiom		⊢
	proveit.logic.equality.substitution
10	instantiation	13, 34, 25	, ⊢
	: , :
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	14, 25, 34, 15, 16, 17^, 18^	, , , , ⊢
	: , : , : , :
13	theorem		⊢
	proveit.numbers.multiplication.commutation
14	theorem		⊢
	proveit.numbers.division.prod_of_fracs
15	instantiation	38, 19, 20	⊢
	: , : , :
16	instantiation	21, 22, 23	, , , ⊢
	: , :
17	instantiation	24, 25	⊢
	:
18	instantiation	26, 27	, ⊢
	:
19	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20	instantiation	38, 28, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.mult_complex_nonzero_closure_bin
22	instantiation	31, 34, 30	, ⊢
	:
23	instantiation	31, 35, 32	, ⊢
	:
24	theorem		⊢
	proveit.numbers.division.frac_one_denom
25	assumption		⊢
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
27	instantiation	33, 34, 35	, ⊢
	: , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
29	instantiation	38, 36, 37	⊢
	: , : , :
30	assumption		⊢
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
32	assumption		⊢
33	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
34	assumption		⊢
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37	instantiation	38, 39, 40	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
^*equality replacement requirements