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^*	, , , ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.exponentiation.products_of_real_powers
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
3	instantiation	10	⊢
	: , : , : , :
4	instantiation	49, 45, 11	⊢
	: , : , :
5	reference	46	⊢
6	reference	27	⊢
7	reference	28	⊢
8	instantiation	12, 13	⊢
	:
9	instantiation	14, 15, 16	, , ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
11	instantiation	49, 17, 19	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
13	instantiation	49, 18, 19	⊢
	: , : , :
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	20, 51, 42, 24, 25	, , ⊢
	: , : , : , : , : , : , :
16	instantiation	21, 33, 34, 35, 22, 23, 42, 24, 25, 26^*	, , ⊢
	: , : , : , : , : , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
19	assumption		⊢
20	theorem		⊢
	proveit.numbers.addition.leftward_commutation
21	theorem		⊢
	proveit.numbers.addition.association
22	instantiation	39	⊢
	: , :
23	instantiation	39	⊢
	: , :
24	instantiation	49, 45, 27	⊢
	: , : , :
25	instantiation	49, 45, 28	⊢
	: , : , :
26	instantiation	29, 30, 31^*	⊢
	: , :
27	assumption		⊢
28	assumption		⊢
29	theorem		⊢
	proveit.logic.equality.equals_reversal
30	instantiation	32, 33, 34, 51, 35, 36, 37, 42, 38^*	⊢
	: , : , : , : , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
32	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
33	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
35	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36	instantiation	39	⊢
	: , :
37	instantiation	49, 45, 40	⊢
	: , : , :
38	instantiation	41, 42	⊢
	:
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	instantiation	49, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
42	instantiation	49, 45, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	49, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
46	assumption		⊢
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	49, 50, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements