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	, ⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 5, 6	, ⊢
	: , : , : , :
3	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
4	instantiation	8, 15, 40, 37, 17, 16, 20, 21, 7	, ⊢
	: , : , : , : , : , :
5	instantiation	8, 40, 15, 16, 9, 17, 20, 21, 23, 22	, ⊢
	: , : , : , : , : , :
6	instantiation	10, 11, 12	, ⊢
	: , : , :
7	instantiation	13, 23, 22	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.disassociation
9	instantiation	25	⊢
	: , :
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	14, 40, 37, 15, 16, 17, 20, 21, 23, 22	, ⊢
	: , : , : , : , : , : , :
12	instantiation	18, 37, 40, 19, 20, 21, 22, 23, 24^*	, ⊢
	: , : , : , : , : , :
13	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
14	theorem		⊢
	proveit.numbers.addition.leftward_commutation
15	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
16	instantiation	25	⊢
	: , :
17	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
18	theorem		⊢
	proveit.numbers.addition.association
19	instantiation	25	⊢
	: , :
20	instantiation	38, 29, 26	⊢
	: , : , :
21	instantiation	38, 29, 27	⊢
	: , : , :
22	instantiation	38, 29, 28	⊢
	: , : , :
23	instantiation	38, 29, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
26	assumption		⊢
27	instantiation	38, 32, 31	⊢
	: , : , :
28	instantiation	38, 32, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	assumption		⊢
31	instantiation	38, 35, 34	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
33	instantiation	38, 35, 36	⊢
	: , : , :
34	instantiation	38, 39, 37	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
36	instantiation	38, 39, 40	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
38	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements