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