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