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^*	, , , ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
2	instantiation	52, 48, 7	⊢
	: , : , :
3	reference	49	⊢
4	instantiation	8, 17, 18, 30, 49, 31	, , ⊢
	: , :
5	instantiation	9, 10	⊢
	:
6	instantiation	19, 11, 12	, , ⊢
	: , : , :
7	instantiation	52, 13, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.add_real_closure
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
10	instantiation	52, 14, 15	⊢
	: , : , :
11	instantiation	16, 54, 17, 36, 18, 38, 45, 27, 28	, , ⊢
	: , : , : , : , : , :
12	instantiation	19, 20, 21	, , ⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
15	assumption		⊢
16	theorem		⊢
	proveit.numbers.addition.disassociation
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
18	instantiation	22	⊢
	: , : , :
19	axiom		⊢
	proveit.logic.equality.equals_transitivity
20	instantiation	23, 54, 45, 27, 28	, , ⊢
	: , : , : , : , : , : , :
21	instantiation	24, 36, 37, 38, 25, 26, 45, 27, 28, 29^*	, , ⊢
	: , : , : , : , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
23	theorem		⊢
	proveit.numbers.addition.leftward_commutation
24	theorem		⊢
	proveit.numbers.addition.association
25	instantiation	42	⊢
	: , :
26	instantiation	42	⊢
	: , :
27	instantiation	52, 48, 30	⊢
	: , : , :
28	instantiation	52, 48, 31	⊢
	: , : , :
29	instantiation	32, 33, 34^*	⊢
	: , :
30	assumption		⊢
31	assumption		⊢
32	theorem		⊢
	proveit.logic.equality.equals_reversal
33	instantiation	35, 36, 37, 54, 38, 39, 40, 45, 41^*	⊢
	: , : , : , : , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
35	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
36	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
38	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
39	instantiation	42	⊢
	: , :
40	instantiation	52, 48, 43	⊢
	: , : , :
41	instantiation	44, 45	⊢
	:
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	instantiation	52, 46, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
45	instantiation	52, 48, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
47	instantiation	52, 50, 51	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	assumption		⊢
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	52, 53, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements