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, 7, 8	⊢
	: , : , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	reference	50	⊢
4	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5	instantiation	9	⊢
	: , :
6	instantiation	12, 10, 11	⊢
	: , :
7	instantiation	12, 13, 14	⊢
	: , :
8	instantiation	15, 16, 17, 18	⊢
	: , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
10	instantiation	52, 31, 19	⊢
	: , : , :
11	instantiation	21, 23, 22	⊢
	: , :
12	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
13	instantiation	52, 31, 20	⊢
	: , : , :
14	instantiation	21, 22, 23	⊢
	: , :
15	theorem		⊢
	proveit.numbers.division.div_complex_closure
16	instantiation	52, 31, 24	⊢
	: , : , :
17	instantiation	52, 31, 25	⊢
	: , : , :
18	instantiation	26, 27	⊢
	:
19	instantiation	52, 40, 28	⊢
	: , : , :
20	instantiation	52, 40, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
22	instantiation	52, 31, 30	⊢
	: , : , :
23	instantiation	52, 31, 32	⊢
	: , : , :
24	instantiation	52, 40, 33	⊢
	: , : , :
25	instantiation	52, 40, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
28	instantiation	52, 48, 35	⊢
	: , : , :
29	instantiation	52, 48, 36	⊢
	: , : , :
30	instantiation	37, 38, 39	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	52, 40, 41	⊢
	: , : , :
33	instantiation	52, 48, 42	⊢
	: , : , :
34	instantiation	52, 48, 43	⊢
	: , : , :
35	instantiation	52, 53, 44	⊢
	: , : , :
36	instantiation	52, 53, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
38	instantiation	46, 47	⊢
	: , :
39	assumption		⊢
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	52, 48, 49	⊢
	: , : , :
42	instantiation	52, 53, 50	⊢
	: , : , :
43	instantiation	52, 53, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
46	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	instantiation	52, 53, 54	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
52	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat1