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^*	⊢
	: , :
1	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
2	instantiation	5, 14	⊢
	:
3	reference	25	⊢
4	instantiation	10, 6, 7	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.negation.complex_closure
6	instantiation	8, 9	⊢
	: , : , :
7	instantiation	10, 11, 12	⊢
	: , : , :
8	axiom		⊢
	proveit.logic.equality.substitution
9	instantiation	13, 14	⊢
	:
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	15, 16, 17, 43, 18, 19, 24, 25, 20	⊢
	: , : , : , : , : , :
12	instantiation	21, 25, 24, 22	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.negation.double_negation
14	instantiation	23, 24, 25	⊢
	: , :
15	theorem		⊢
	proveit.numbers.addition.disassociation
16	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
18	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
19	instantiation	26	⊢
	: , :
20	instantiation	41, 29, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
22	instantiation	28	⊢
	:
23	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
24	assumption		⊢
25	instantiation	41, 29, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27	instantiation	41, 31, 32	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.equality.equals_reflexivity
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	instantiation	41, 33, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
32	instantiation	41, 35, 36	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
34	instantiation	41, 37, 38	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
36	instantiation	41, 39, 40	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
38	instantiation	41, 42, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
40	instantiation	44, 45	⊢
	:
41	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
44	theorem		⊢
	proveit.numbers.negation.int_neg_closure
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
^*equality replacement requirements