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.logic.equality.four_chain_transitivity
2	instantiation	20, 5, 6	⊢
	: , : , :
3	instantiation	7, 24, 32, 33, 8	⊢
	: , : , :
4	instantiation	42	⊢
	:
5	instantiation	26, 51, 61, 27, 9, 29, 18, 30	⊢
	: , : , : , : , : , :
6	instantiation	20, 10, 11	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
8	instantiation	12, 13, 14	⊢
	: , : , :
9	instantiation	37	⊢
	: , :
10	instantiation	15, 51, 27, 29, 18, 30	⊢
	: , : , : , : , : , : , :
11	instantiation	16, 27, 61, 51, 29, 17, 18, 30, 19^*	⊢
	: , : , : , : , : , :
12	theorem		⊢
	proveit.logic.equality.sub_right_side_into
13	instantiation	20, 21, 22	⊢
	: , : , :
14	instantiation	23, 32, 24	⊢
	: , :
15	theorem		⊢
	proveit.numbers.addition.leftward_commutation
16	theorem		⊢
	proveit.numbers.addition.association
17	instantiation	37	⊢
	: , :
18	instantiation	62, 40, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	26, 51, 61, 27, 28, 29, 32, 30, 33	⊢
	: , : , : , : , : , :
22	instantiation	31, 32, 33, 34	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.commutation
24	instantiation	62, 40, 35	⊢
	: , : , :
25	instantiation	62, 48, 36	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.disassociation
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	instantiation	37	⊢
	: , :
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	instantiation	62, 40, 38	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
32	instantiation	62, 40, 39	⊢
	: , : , :
33	instantiation	62, 40, 41	⊢
	: , : , :
34	instantiation	42	⊢
	:
35	instantiation	62, 48, 43	⊢
	: , : , :
36	instantiation	62, 54, 44	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
38	instantiation	62, 48, 45	⊢
	: , : , :
39	instantiation	46, 47, 64	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	62, 48, 49	⊢
	: , : , :
42	axiom		⊢
	proveit.logic.equality.equals_reflexivity
43	instantiation	62, 54, 50	⊢
	: , : , :
44	instantiation	62, 60, 51	⊢
	: , : , :
45	instantiation	62, 54, 56	⊢
	: , : , :
46	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
47	instantiation	52, 53	⊢
	: , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
49	instantiation	62, 54, 57	⊢
	: , : , :
50	instantiation	55, 56, 57	⊢
	: , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
52	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
55	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
56	instantiation	58, 59	⊢
	:
57	instantiation	62, 60, 61	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.negation.int_closure
59	instantiation	62, 63, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
64	assumption		⊢
^*equality replacement requirements