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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	6, 4, 49, 7, 10, 8, 5, 11, 12, 13	, , , ⊢
	: , : , : , : , : , :
3	instantiation	6, 7, 52, 49, 8, 9, 10, 15, 16, 11, 12, 13	, , , ⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
5	instantiation	14, 15, 16	⊢
	: , :
6	theorem		⊢
	proveit.numbers.multiplication.disassociation
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	17	⊢
	: , :
10	instantiation	18	⊢
	: , : , :
11	instantiation	50, 36, 19	⊢
	: , : , :
12	instantiation	50, 36, 20	⊢
	: , : , :
13	instantiation	50, 36, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
15	instantiation	22, 23, 24, 25	⊢
	: , :
16	instantiation	26, 27, 28	⊢
	: , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
19	instantiation	50, 40, 29	⊢
	: , : , :
20	instantiation	50, 40, 30	⊢
	: , : , :
21	assumption		⊢
22	theorem		⊢
	proveit.numbers.division.div_complex_closure
23	instantiation	50, 36, 31	⊢
	: , : , :
24	instantiation	50, 36, 32	⊢
	: , : , :
25	instantiation	33, 34	⊢
	:
26	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
27	instantiation	50, 36, 35	⊢
	: , : , :
28	instantiation	50, 36, 37	⊢
	: , : , :
29	assumption		⊢
30	assumption		⊢
31	instantiation	50, 42, 38	⊢
	: , : , :
32	instantiation	50, 42, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
35	instantiation	50, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	50, 42, 43	⊢
	: , : , :
38	instantiation	50, 46, 44	⊢
	: , : , :
39	instantiation	50, 46, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
41	assumption		⊢
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	50, 46, 47	⊢
	: , : , :
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.nat4
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
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.nat2