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	37	⊢
2	instantiation	4, 5, 6, 7, 8, 9	⊢
	: , : , : , :
3	instantiation	37, 10, 11	⊢
	: , : , :
4	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
6	instantiation	12	⊢
	: , : , : , :
7	instantiation	12	⊢
	: , : , : , :
8	instantiation	13, 29, 15	⊢
	: , : , :
9	instantiation	14, 29, 19, 15	⊢
	: , : , :
10	instantiation	16, 26, 50, 25, 28, 27, 29, 19	⊢
	: , : , : , : , : , : , :
11	instantiation	24, 25, 17, 50, 27, 18, 29, 19, 20^*	⊢
	: , : , : , : , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
13	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
14	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
15	instantiation	21	⊢
	:
16	theorem		⊢
	proveit.numbers.addition.leftward_commutation
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
18	instantiation	22	⊢
	: , : , :
19	instantiation	48, 35, 23	⊢
	: , : , :
20	instantiation	24, 25, 26, 50, 27, 28, 29, 30^*	⊢
	: , : , : , : , : , :
21	axiom		⊢
	proveit.logic.equality.equals_reflexivity
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
23	instantiation	31, 32, 33	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.association
25	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
27	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28	instantiation	34	⊢
	: , :
29	instantiation	48, 35, 36	⊢
	: , : , :
30	instantiation	37, 38, 39	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
32	instantiation	40, 41	⊢
	: , :
33	assumption		⊢
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
36	instantiation	48, 42, 43	⊢
	: , : , :
37	axiom		⊢
	proveit.logic.equality.equals_transitivity
38	instantiation	44, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
40	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_within_real
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	48, 46, 47	⊢
	: , : , :
44	axiom		⊢
	proveit.logic.equality.substitution
45	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	48, 49, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements