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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8, 9	⊢
	: , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	theorem		⊢
	proveit.numbers.negation.negated_zero
6	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
7	instantiation	10, 11, 16, 12, 17, 13, 21, 18, 14, 20	⊢
	: , : , : , : , : , :
8	instantiation	15, 16, 46, 17, 21, 18, 20	⊢
	: , : , : , :
9	instantiation	19, 20, 21, 22	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.addition.disassociation
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	instantiation	23	⊢
	: , :
14	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
15	theorem		⊢
	proveit.numbers.addition.elim_zero_any
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
17	instantiation	23	⊢
	: , :
18	instantiation	44, 26, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
20	instantiation	44, 26, 25	⊢
	: , : , :
21	instantiation	44, 26, 27	⊢
	: , : , :
22	instantiation	28	⊢
	:
23	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
24	instantiation	44, 29, 30	⊢
	: , : , :
25	instantiation	44, 31, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
27	instantiation	33, 34, 35	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.equality.equals_reflexivity
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
30	instantiation	44, 36, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
32	instantiation	44, 38, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
34	instantiation	40, 41	⊢
	: , :
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
37	instantiation	44, 42, 43	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	44, 45, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
43	instantiation	47, 48	⊢
	:
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
47	theorem		⊢
	proveit.numbers.negation.int_neg_closure
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1