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	4, 29, 36, 7, 9, 8, 5, 10, 11	⊢
	: , : , : , : , : , :
3	instantiation	6, 7, 36, 8, 9, 10, 11	⊢
	: , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.disassociation
5	instantiation	47, 27, 12	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
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	13	⊢
	: , :
10	instantiation	15, 16, 14	⊢
	: , :
11	instantiation	15, 16, 17	⊢
	: , :
12	instantiation	47, 33, 18	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	instantiation	47, 27, 19	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
16	instantiation	47, 27, 20	⊢
	: , : , :
17	instantiation	21, 22	⊢
	:
18	instantiation	47, 31, 23	⊢
	: , : , :
19	instantiation	24, 25	⊢
	:
20	instantiation	47, 33, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.negation.complex_closure
22	instantiation	47, 27, 28	⊢
	: , : , :
23	instantiation	47, 35, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.negation.real_closure
25	instantiation	47, 33, 30	⊢
	: , : , :
26	instantiation	47, 31, 32	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
28	instantiation	47, 33, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
30	instantiation	47, 37, 40	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
32	instantiation	47, 35, 36	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
34	instantiation	47, 37, 38	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
38	instantiation	39, 40, 41	⊢
	: , :
39	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
40	instantiation	42, 43, 44	⊢
	: , :
41	instantiation	47, 48, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
43	instantiation	47, 48, 46	⊢
	: , : , :
44	instantiation	47, 48, 49	⊢
	: , : , :
45	assumption		⊢
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2