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	generalization	1	⊢
1	instantiation	2, 3, 4	⊢
	: , :
2	theorem		⊢
	proveit.logic.equality.lhs_via_equality
3	instantiation	5, 6, 7	⊢
	: , :
4	instantiation	8	⊢
	: , : , : , :
5	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
6	axiom		⊢
	proveit.logic.booleans.true_axiom
7	assumption		⊢
8	instantiation	9, 21, 10^, 11^, 12^*	⊢
	:
9	axiom		⊢
	proveit.core_expr_types.tuples.tuple_eq_def
10	instantiation	14, 21, 44, 15, 13, 26	⊢
	: , : , : , : , : , : , :
11	instantiation	14, 21, 44, 15, 16, 27	⊢
	: , : , : , : , : , : , :
12	instantiation	17, 18, 19	⊢
	: , : , :
13	instantiation	20, 21	⊢
	: , :
14	theorem		⊢
	proveit.core_expr_types.tuples.tuple_portion_substitution
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	20, 21	⊢
	: , :
17	axiom		⊢
	proveit.logic.equality.equals_transitivity
18	instantiation	22, 23, 24, 25, 26, 27	⊢
	: , : , : , :
19	instantiation	28, 29	⊢
	:
20	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
21	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
22	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
24	instantiation	30	⊢
	: , :
25	instantiation	30	⊢
	: , :
26	instantiation	31, 32	⊢
	: , : , :
27	instantiation	31, 32	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.booleans.eq_true_intro
29	instantiation	33	⊢
	:
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	axiom		⊢
	proveit.core_expr_types.tuples.empty_range_def
32	instantiation	34, 35	⊢
	:
33	axiom		⊢
	proveit.logic.equality.equals_reflexivity
34	theorem		⊢
	proveit.numbers.addition.elim_zero_left
35	instantiation	42, 36, 37	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	42, 38, 39	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
39	instantiation	42, 40, 41	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	42, 43, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements