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	5, 6, 46, 52, 9, 7, 10, 11, 12, 4	, , ⊢
	: , : , : , : , : , :
3	instantiation	5, 46, 47, 6, 7, 8, 9, 10, 11, 12, 14, 15	, , ⊢
	: , : , : , : , : , :
4	instantiation	13, 14, 15	⊢
	: , :
5	theorem		⊢
	proveit.numbers.multiplication.disassociation
6	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
7	instantiation	16	⊢
	: , : , :
8	instantiation	17	⊢
	: , :
9	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10	instantiation	20, 18, 21, 19	⊢
	: , :
11	assumption		⊢
12	assumption		⊢
13	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
14	instantiation	20, 21, 22, 23	⊢
	: , :
15	instantiation	24, 25, 26	⊢
	: , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	instantiation	50, 33, 27	⊢
	: , : , :
19	instantiation	31, 28	⊢
	:
20	theorem		⊢
	proveit.numbers.division.div_complex_closure
21	instantiation	50, 33, 29	⊢
	: , : , :
22	instantiation	50, 33, 30	⊢
	: , : , :
23	instantiation	31, 32	⊢
	:
24	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
25	assumption		⊢
26	instantiation	50, 33, 34	⊢
	: , : , :
27	instantiation	50, 43, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
29	instantiation	50, 43, 36	⊢
	: , : , :
30	instantiation	50, 43, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	38, 39	⊢
	:
35	instantiation	50, 48, 40	⊢
	: , : , :
36	instantiation	50, 48, 41	⊢
	: , : , :
37	instantiation	50, 48, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.negation.real_closure
39	instantiation	50, 43, 44	⊢
	: , : , :
40	instantiation	50, 51, 45	⊢
	: , : , :
41	instantiation	50, 51, 46	⊢
	: , : , :
42	instantiation	50, 51, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	50, 48, 49	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	instantiation	50, 51, 52	⊢
	: , : , :
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.nat1