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, 11, 12, 13, 14^*	, , , ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.association
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	instantiation	15	⊢
	: , :
7	instantiation	16	⊢
	: , : , : , : , :
8	reference	37	⊢
9	instantiation	51, 42, 17	⊢
	: , : , :
10	instantiation	51, 42, 18	⊢
	: , : , :
11	instantiation	19, 20, 21, 22	⊢
	: , :
12	instantiation	51, 42, 23	⊢
	: , : , :
13	instantiation	51, 42, 24	⊢
	: , : , :
14	instantiation	25, 37, 26, 27^, 28^	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
17	instantiation	51, 48, 29	⊢
	: , : , :
18	instantiation	51, 40, 30	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.division.div_complex_closure
20	instantiation	51, 42, 31	⊢
	: , : , :
21	instantiation	51, 42, 32	⊢
	: , : , :
22	instantiation	33, 34	⊢
	:
23	instantiation	51, 48, 35	⊢
	: , : , :
24	assumption		⊢
25	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
27	instantiation	36, 37	⊢
	:
28	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
29	assumption		⊢
30	instantiation	51, 46, 38	⊢
	: , : , :
31	instantiation	51, 40, 39	⊢
	: , : , :
32	instantiation	51, 40, 41	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
37	instantiation	51, 42, 43	⊢
	: , : , :
38	instantiation	51, 52, 44	⊢
	: , : , :
39	instantiation	51, 46, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	51, 46, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
43	instantiation	51, 48, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
45	instantiation	51, 52, 50	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	51, 52, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
49	assumption		⊢
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements