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, 9, 10	⊢
	: , : , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
2	reference	55	⊢
3	reference	37	⊢
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	11	⊢
	: , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	instantiation	53, 34, 12	⊢
	: , : , :
8	instantiation	15, 13, 14	⊢
	: , :
9	instantiation	15, 16, 17	⊢
	: , :
10	instantiation	18, 26, 19, 20	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12	instantiation	53, 43, 21	⊢
	: , : , :
13	instantiation	53, 34, 22	⊢
	: , : , :
14	instantiation	24, 26, 25	⊢
	: , :
15	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
16	instantiation	53, 34, 23	⊢
	: , : , :
17	instantiation	24, 25, 26	⊢
	: , :
18	theorem		⊢
	proveit.numbers.division.div_complex_closure
19	instantiation	53, 34, 27	⊢
	: , : , :
20	instantiation	28, 29	⊢
	:
21	instantiation	53, 50, 30	⊢
	: , : , :
22	instantiation	53, 43, 31	⊢
	: , : , :
23	instantiation	53, 43, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
25	instantiation	53, 34, 33	⊢
	: , : , :
26	instantiation	53, 34, 35	⊢
	: , : , :
27	instantiation	53, 43, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
30	instantiation	53, 54, 37	⊢
	: , : , :
31	instantiation	53, 50, 38	⊢
	: , : , :
32	instantiation	53, 50, 39	⊢
	: , : , :
33	instantiation	40, 41, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	53, 43, 44	⊢
	: , : , :
36	instantiation	53, 50, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
38	instantiation	53, 54, 46	⊢
	: , : , :
39	instantiation	53, 54, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
41	instantiation	48, 49	⊢
	: , :
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	53, 50, 51	⊢
	: , : , :
45	instantiation	53, 54, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
48	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	53, 54, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1