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	8	⊢
2	instantiation	25, 11, 4	, ⊢
	: , :
3	instantiation	5, 6, 7	, ⊢
	: , : , :
4	instantiation	8, 9, 10	, ⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.equals_transitivity
6	instantiation	16, 18, 12, 17, 14, 19, 11, 26, 27, 21	, ⊢
	: , : , : , : , : , :
7	instantiation	16, 17, 45, 12, 19, 13, 14, 22, 23, 26, 27, 21	, ⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.logic.equality.sub_right_side_into
9	instantiation	25, 15, 21	, ⊢
	: , :
10	instantiation	16, 17, 45, 18, 19, 20, 26, 27, 21	, ⊢
	: , : , : , : , : , :
11	instantiation	25, 22, 23	⊢
	: , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
13	instantiation	28	⊢
	: , :
14	instantiation	24	⊢
	: , : , :
15	instantiation	25, 26, 27	⊢
	: , :
16	theorem		⊢
	proveit.numbers.multiplication.disassociation
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	28	⊢
	: , :
21	instantiation	43, 32, 29	⊢
	: , : , :
22	instantiation	43, 32, 30	⊢
	: , : , :
23	instantiation	43, 32, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
25	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
26	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
27	instantiation	43, 32, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	instantiation	43, 35, 34	⊢
	: , : , :
30	instantiation	43, 35, 36	⊢
	: , : , :
31	instantiation	43, 38, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	43, 38, 39	⊢
	: , : , :
34	instantiation	43, 41, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	43, 41, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
39	assumption		⊢
40	assumption		⊢
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	43, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat2