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	⊢
	: , :
1	theorem		⊢
	proveit.logic.equality.equals_reversal
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 7	⊢
	: , : , :
5	instantiation	8, 9, 10, 11	⊢
	: , : , : , :
6	axiom		⊢
	proveit.logic.equality.substitution
7	instantiation	12, 13, 46, 14^*	⊢
	: , :
8	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
9	instantiation	15, 59, 64, 16, 17, 28, 40, 39	⊢
	: , : , : , : , : , :
10	instantiation	18, 22, 19, 24, 20, 28, 40, 39	⊢
	: , : , : , :
11	instantiation	21, 59, 64, 22, 23, 24, 28, 40, 39, 25^*	⊢
	: , : , : , : , : , :
12	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
13	instantiation	62, 52, 26	⊢
	: , : , :
14	instantiation	27, 28	⊢
	:
15	theorem		⊢
	proveit.numbers.addition.disassociation
16	instantiation	30	⊢
	: , :
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
18	theorem		⊢
	proveit.numbers.addition.elim_zero_any
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
20	instantiation	29	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.association
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	instantiation	30	⊢
	: , :
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	instantiation	31, 32, 33	⊢
	: , : , :
26	instantiation	62, 57, 34	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.negation.double_negation
28	instantiation	62, 52, 35	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	theorem		⊢
	proveit.logic.equality.sub_right_side_into
32	instantiation	36, 39, 46, 37	⊢
	: , : , :
33	instantiation	38, 39, 40	⊢
	: , :
34	instantiation	62, 60, 41	⊢
	: , : , :
35	instantiation	42, 43, 55	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
37	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
38	theorem		⊢
	proveit.numbers.addition.commutation
39	instantiation	62, 52, 44	⊢
	: , : , :
40	instantiation	45, 46	⊢
	:
41	instantiation	47, 48	⊢
	:
42	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
43	instantiation	49, 50	⊢
	: , :
44	instantiation	62, 57, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.negation.complex_closure
46	instantiation	62, 52, 53	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.negation.int_closure
48	instantiation	62, 54, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
51	instantiation	62, 60, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
53	instantiation	62, 57, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
55	assumption		⊢
56	instantiation	62, 63, 59	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
58	instantiation	62, 60, 61	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
61	instantiation	62, 63, 64	⊢
	: , : , :
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements