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^*	, , , ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.addition.association
2	reference	52	⊢
3	reference	49	⊢
4	instantiation	37	⊢
	: , :
5	instantiation	37	⊢
	: , :
6	instantiation	50, 44, 11	⊢
	: , : , :
7	reference	40	⊢
8	instantiation	13, 22, 12	⊢
	: , :
9	instantiation	13, 14, 15	⊢
	: , :
10	instantiation	16, 17, 18^*	⊢
	: , :
11	instantiation	50, 35, 19	⊢
	: , : , :
12	instantiation	50, 44, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
14	instantiation	21, 29, 22, 23	⊢
	: , :
15	instantiation	50, 44, 24	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.equality.equals_reversal
17	instantiation	25, 26, 49, 52, 27, 28, 29, 40, 30^*	⊢
	: , : , : , : , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
19	assumption		⊢
20	instantiation	50, 35, 31	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.division.div_complex_closure
22	instantiation	50, 44, 32	⊢
	: , : , :
23	instantiation	33, 34	⊢
	:
24	instantiation	50, 35, 36	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
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	37	⊢
	: , :
29	instantiation	50, 44, 38	⊢
	: , : , :
30	instantiation	39, 40	⊢
	:
31	assumption		⊢
32	instantiation	50, 42, 41	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
36	assumption		⊢
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
38	instantiation	50, 42, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
40	instantiation	50, 44, 45	⊢
	: , : , :
41	instantiation	50, 47, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	50, 47, 48	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	assumption		⊢
46	instantiation	50, 51, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	50, 51, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
50	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements