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	reference	27	⊢
2	instantiation	4, 5	, ⊢
	: , : , :
3	instantiation	6, 7	, ⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 36, 9, 33, 37, 10, 43, 44, 40, 41, 11	, ⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.logic.equality.equals_reversal
7	instantiation	12, 13, 14, 15	, ⊢
	: , :
8	theorem		⊢
	proveit.numbers.multiplication.association
9	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
10	instantiation	16	⊢
	: , : , : , :
11	instantiation	57, 48, 17	⊢
	: , : , :
12	instantiation	18, 32	⊢
	:
13	instantiation	57, 48, 19	⊢
	: , : , :
14	instantiation	20, 21, 22	⊢
	: , : , :
15	instantiation	23, 24	⊢
	:
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
17	instantiation	57, 51, 25	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.exponentiation.int_exp_of_exp
19	instantiation	57, 53, 31	⊢
	: , : , :
20	theorem		⊢
	proveit.logic.equality.sub_right_side_into
21	instantiation	42, 34, 26	⊢
	: , :
22	instantiation	27, 28, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
24	instantiation	57, 30, 31	⊢
	: , : , :
25	instantiation	57, 55, 32	⊢
	: , : , :
26	instantiation	42, 40, 41	⊢
	: , :
27	axiom		⊢
	proveit.logic.equality.equals_transitivity
28	instantiation	35, 33, 59, 36, 39, 37, 34, 40, 41	⊢
	: , : , : , : , : , :
29	instantiation	35, 36, 59, 37, 38, 39, 43, 44, 40, 41	⊢
	: , : , : , : , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
32	assumption		⊢
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
34	instantiation	42, 43, 44	⊢
	: , :
35	theorem		⊢
	proveit.numbers.multiplication.disassociation
36	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
37	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38	instantiation	45	⊢
	: , :
39	instantiation	45	⊢
	: , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
41	instantiation	57, 48, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
43	instantiation	57, 48, 47	⊢
	: , : , :
44	instantiation	57, 48, 49	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46	instantiation	57, 53, 50	⊢
	: , : , :
47	instantiation	57, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	57, 53, 54	⊢
	: , : , :
50	assumption		⊢
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
52	instantiation	57, 55, 56	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	57, 58, 59	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat2