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^*	, , ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.exponentiation.products_of_real_powers
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
3	instantiation	9	⊢
	: , : , :
4	instantiation	45, 41, 10	⊢
	: , : , :
5	reference	42	⊢
6	reference	24	⊢
7	instantiation	11, 12	⊢
	:
8	instantiation	13, 14, 15	, ⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
10	instantiation	45, 16, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
12	instantiation	45, 17, 18	⊢
	: , : , :
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	19, 47, 29, 31, 38, 22	, ⊢
	: , : , : , : , : , : , :
15	instantiation	20, 29, 30, 47, 31, 21, 38, 22, 23^*	, ⊢
	: , : , : , : , : , :
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
18	assumption		⊢
19	theorem		⊢
	proveit.numbers.addition.leftward_commutation
20	theorem		⊢
	proveit.numbers.addition.association
21	instantiation	35	⊢
	: , :
22	instantiation	45, 41, 24	⊢
	: , : , :
23	instantiation	25, 26, 27^*	⊢
	: , :
24	assumption		⊢
25	theorem		⊢
	proveit.logic.equality.equals_reversal
26	instantiation	28, 29, 30, 47, 31, 32, 33, 38, 34^*	⊢
	: , : , : , : , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
28	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	instantiation	35	⊢
	: , :
33	instantiation	45, 41, 36	⊢
	: , : , :
34	instantiation	37, 38	⊢
	:
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	instantiation	45, 39, 40	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
38	instantiation	45, 41, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	45, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	instantiation	45, 46, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements