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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.core_expr_types.tuples.range_len
5	instantiation	55, 33, 9	⊢
	: , : , :
6	axiom		⊢
	proveit.logic.equality.equals_transitivity
7	instantiation	10, 45	⊢
	: , : , :
8	instantiation	11, 12, 13, 14	⊢
	: , : , : , :
9	instantiation	15, 26, 27, 16, 29, 17, 18, 57, 19	⊢
	: , : , : , : , :
10	axiom		⊢
	proveit.logic.equality.substitution
11	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
12	instantiation	20, 27, 26, 29, 24, 21, 30, 31, 22	⊢
	: , : , : , : , : , :
13	instantiation	23, 26, 57, 24, 30, 31	⊢
	: , : , : , :
14	instantiation	25, 57, 26, 27, 28, 29, 30, 31, 32^*	⊢
	: , : , : , : , : , :
15	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
16	instantiation	37	⊢
	: , :
17	instantiation	55, 33, 34	⊢
	: , : , :
18	instantiation	46, 35, 36	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
20	theorem		⊢
	proveit.numbers.addition.disassociation
21	instantiation	37	⊢
	: , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
23	theorem		⊢
	proveit.numbers.addition.elim_zero_any
24	instantiation	37	⊢
	: , :
25	theorem		⊢
	proveit.numbers.addition.association
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
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	55, 39, 38	⊢
	: , : , :
31	instantiation	55, 39, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
34	instantiation	41, 48, 42	⊢
	: , :
35	instantiation	51, 43	⊢
	: , :
36	instantiation	44, 45	⊢
	: , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
38	instantiation	46, 47, 48	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	instantiation	55, 49, 50	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
43	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
44	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
45	theorem		⊢
	proveit.numbers.negation.negated_zero
46	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
47	instantiation	51, 52	⊢
	: , :
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	55, 53, 54	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
54	instantiation	55, 56, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements