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^*	, , ⊢
	: , : , : , : , : , :
1	reference	25	⊢
2	reference	48	⊢
3	reference	22	⊢
4	instantiation	36	⊢
	: , :
5	instantiation	33	⊢
	: , : , :
6	instantiation	36	⊢
	: , :
7	instantiation	12, 13, 14	⊢
	: , :
8	instantiation	51, 37, 15	⊢
	: , : , :
9	reference	35	⊢
10	assumption		⊢
11	instantiation	16, 17, 18^*	⊢
	: , :
12	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
13	instantiation	51, 37, 19	⊢
	: , : , :
14	assumption		⊢
15	instantiation	51, 44, 20	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.equality.equals_reversal
17	instantiation	21, 26, 22, 53, 27, 23, 29, 35, 24^*	⊢
	: , : , : , : , : , :
18	instantiation	25, 26, 48, 53, 27, 28, 29, 30^*	⊢
	: , : , : , : , : , :
19	instantiation	51, 44, 31	⊢
	: , : , :
20	instantiation	51, 49, 32	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
23	instantiation	33	⊢
	: , : , :
24	instantiation	34, 35	⊢
	:
25	theorem		⊢
	proveit.numbers.addition.association
26	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
27	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28	instantiation	36	⊢
	: , :
29	instantiation	51, 37, 38	⊢
	: , : , :
30	instantiation	39, 40, 41	⊢
	: , : , :
31	instantiation	51, 49, 42	⊢
	: , : , :
32	instantiation	51, 52, 43	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
34	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
38	instantiation	51, 44, 45	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.equals_transitivity
40	instantiation	46, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
42	instantiation	51, 52, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	51, 49, 50	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.substitution
47	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	51, 52, 53	⊢
	: , : , :
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.nat1
^*equality replacement requirements