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, 4, 5, 6	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.divisibility.common_factor_elimination
2	reference	31	⊢
3	reference	16	⊢
4	instantiation	7, 29, 30	⊢
	: , :
5	instantiation	13, 8, 9	⊢
	: , : , :
6	instantiation	10, 11, 12	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
8	instantiation	13, 14, 15	⊢
	: , : , :
9	instantiation	24, 25, 48, 26, 27, 28, 29, 30, 16	⊢
	: , : , : , : , : , :
10	theorem		⊢
	proveit.logic.equality.sub_left_side_into
11	instantiation	17, 18	⊢
	:
12	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_4
13	theorem		⊢
	proveit.logic.equality.sub_right_side_into
14	assumption		⊢
15	instantiation	19, 20, 21	⊢
	: , : , :
16	instantiation	50, 36, 22	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
19	axiom		⊢
	proveit.logic.equality.equals_transitivity
20	instantiation	23, 26, 25, 27, 29, 31, 30	⊢
	: , : , : , : , : , : , :
21	instantiation	24, 25, 48, 26, 27, 28, 29, 30, 31	⊢
	: , : , : , : , : , :
22	instantiation	50, 41, 32	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
24	theorem		⊢
	proveit.numbers.multiplication.association
25	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
27	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28	instantiation	33	⊢
	: , :
29	instantiation	50, 36, 34	⊢
	: , : , :
30	instantiation	50, 36, 35	⊢
	: , : , :
31	instantiation	50, 36, 37	⊢
	: , : , :
32	instantiation	50, 46, 38	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34	instantiation	50, 41, 39	⊢
	: , : , :
35	instantiation	50, 41, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	50, 41, 42	⊢
	: , : , :
38	instantiation	50, 51, 43	⊢
	: , : , :
39	instantiation	50, 46, 44	⊢
	: , : , :
40	instantiation	50, 46, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	50, 46, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
44	instantiation	50, 51, 48	⊢
	: , : , :
45	instantiation	50, 51, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	50, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
50	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat3