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, 8^*	, , , , ⊢
	: , : , :
4	instantiation	13, 28, 29, 31	, , , , ⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.equals_transitivity
6	instantiation	9, 10	, ⊢
	: , : , :
7	instantiation	11, 12	, , , , ⊢
	: , :
8	instantiation	13, 28, 29, 14, 15^*	, , , ⊢
	: , : , :
9	axiom		⊢
	proveit.logic.equality.substitution
10	instantiation	16, 42, 31	, ⊢
	: , :
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	17, 31, 42, 18, 19, 20^, 21^	, , , , ⊢
	: , : , : , :
13	theorem		⊢
	proveit.numbers.division.frac_cancel_left
14	instantiation	50, 22, 23	⊢
	: , : , :
15	instantiation	24, 42	⊢
	:
16	theorem		⊢
	proveit.numbers.multiplication.commutation
17	theorem		⊢
	proveit.numbers.division.prod_of_fracs
18	instantiation	50, 25, 26	⊢
	: , : , :
19	instantiation	27, 28, 29	, , , ⊢
	: , :
20	instantiation	30, 31	⊢
	:
21	instantiation	32, 33	, ⊢
	:
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
23	instantiation	50, 34, 35	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
25	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
26	instantiation	50, 36, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.multiplication.mult_complex_nonzero_closure_bin
28	instantiation	39, 42, 38	, ⊢
	:
29	instantiation	39, 43, 40	, ⊢
	:
30	theorem		⊢
	proveit.numbers.division.frac_one_denom
31	assumption		⊢
32	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
33	instantiation	41, 42, 43	, ⊢
	: , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	50, 44, 45	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
37	instantiation	50, 46, 47	⊢
	: , : , :
38	assumption		⊢
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
40	assumption		⊢
41	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
42	assumption		⊢
43	assumption		⊢
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
45	instantiation	50, 48, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
47	instantiation	50, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
50	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
^*equality replacement requirements