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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 51, 54, 5, 9, 42, 10, 11	, , , ⊢
	: , : , : , : , : , : , :
3	instantiation	6, 54, 51, 7, 8, 9, 42, 10, 11, 12^*	, , , ⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.addition.leftward_commutation
5	instantiation	39	⊢
	: , :
6	theorem		⊢
	proveit.numbers.addition.association
7	instantiation	39	⊢
	: , :
8	instantiation	39	⊢
	: , :
9	instantiation	52, 46, 13	⊢
	: , : , :
10	instantiation	15, 24, 14	⊢
	: , :
11	instantiation	15, 16, 17	⊢
	: , :
12	instantiation	18, 19, 20^*	⊢
	: , :
13	instantiation	52, 37, 21	⊢
	: , : , :
14	instantiation	52, 46, 22	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
16	instantiation	23, 31, 24, 25	⊢
	: , :
17	instantiation	52, 46, 26	⊢
	: , : , :
18	theorem		⊢
	proveit.logic.equality.equals_reversal
19	instantiation	27, 28, 51, 54, 29, 30, 31, 42, 32^*	⊢
	: , : , : , : , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
21	assumption		⊢
22	instantiation	52, 37, 33	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.division.div_complex_closure
24	instantiation	52, 46, 34	⊢
	: , : , :
25	instantiation	35, 36	⊢
	:
26	instantiation	52, 37, 38	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
28	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	instantiation	39	⊢
	: , :
31	instantiation	52, 46, 40	⊢
	: , : , :
32	instantiation	41, 42	⊢
	:
33	assumption		⊢
34	instantiation	52, 44, 43	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
38	assumption		⊢
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	instantiation	52, 44, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
42	instantiation	52, 46, 47	⊢
	: , : , :
43	instantiation	52, 49, 48	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	52, 49, 50	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	assumption		⊢
48	instantiation	52, 53, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	52, 53, 54	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
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