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, 5, 6, 7^*	, , , , ⊢
	: , : , :
1	axiom		⊢
	proveit.numbers.ordering.min_def_multi
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
3	instantiation	40	⊢
	: , :
4	reference	48	⊢
5	reference	47	⊢
6	reference	38	⊢
7	instantiation	24, 8, 9	, , , , ⊢
	: , : , :
8	instantiation	10, 11	, , ⊢
	: , : , :
9	instantiation	18, 47, 38, 12^*	, , ⊢
	: , :
10	axiom		⊢
	proveit.logic.equality.substitution
11	instantiation	24, 13, 14	, , ⊢
	: , : , :
12	instantiation	24, 15, 16	, , ⊢
	: , : , :
13	instantiation	17, 48, 47	, ⊢
	: , :
14	instantiation	18, 47, 48, 19^*	, , ⊢
	: , :
15	instantiation	28, 29, 20, 21, 22, 23	, , ⊢
	: , : , : , :
16	instantiation	34, 35, 36, 37	⊢
	: , : , : , : , :
17	theorem		⊢
	proveit.numbers.ordering.min_bin_args_commute
18	axiom		⊢
	proveit.numbers.ordering.min_def_bin
19	instantiation	24, 25, 26	, , ⊢
	: , : , :
20	instantiation	40	⊢
	: , :
21	instantiation	40	⊢
	: , :
22	instantiation	41, 39	⊢
	: , :
23	instantiation	42, 27	, , ⊢
	: , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	28, 29, 30, 31, 32, 33	, , ⊢
	: , : , : , :
26	instantiation	34, 35, 36, 37	⊢
	: , : , : , : , :
27	instantiation	46, 47, 38, 39	, , ⊢
	: , :
28	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
30	instantiation	40	⊢
	: , :
31	instantiation	40	⊢
	: , :
32	instantiation	41, 49	⊢
	: , :
33	instantiation	42, 43	, , ⊢
	: , :
34	axiom		⊢
	proveit.core_expr_types.conditionals.true_case_reduction
35	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
37	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38	assumption		⊢
39	instantiation	44, 45	⊢
	: , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
41	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
42	theorem		⊢
	proveit.core_expr_types.conditionals.dissatisfied_condition_reduction
43	instantiation	46, 47, 48, 49	, , ⊢
	: , :
44	theorem		⊢
	proveit.numbers.ordering.relax_less
45	assumption		⊢
46	theorem		⊢
	proveit.numbers.ordering.not_less_from_less_eq
47	assumption		⊢
48	assumption		⊢
49	assumption		⊢
^*equality replacement requirements