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	24, 6, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.core_expr_types.tuples.range_len
5	instantiation	8, 9, 10, 43, 11	⊢
	: , :
6	instantiation	31, 30	⊢
	: , : , :
7	instantiation	12, 13, 14, 43, 15, 16, 34, 17, 18^*	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.numbers.addition.add_nat_closure
9	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
10	instantiation	19	⊢
	: , : , :
11	instantiation	20, 21, 22	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.association
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	23	⊢
	: , :
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
18	instantiation	24, 25, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
20	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
21	instantiation	27, 28	⊢
	: , :
22	instantiation	29, 30	⊢
	: , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	31, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
27	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
29	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
30	theorem		⊢
	proveit.numbers.negation.negated_zero
31	axiom		⊢
	proveit.logic.equality.substitution
32	instantiation	33, 34	⊢
	:
33	theorem		⊢
	proveit.numbers.addition.elim_zero_right
34	instantiation	41, 35, 36	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
36	instantiation	41, 37, 38	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	41, 39, 40	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	41, 42, 43	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements