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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_3
3	instantiation	5	⊢
	:
4	instantiation	6, 7	⊢
	: , :
5	axiom		⊢
	proveit.logic.equality.equals_reflexivity
6	theorem		⊢
	proveit.logic.equality.equals_reversal
7	instantiation	17, 18, 32, 19, 8, 9, 22, 10, 21, 11^*	⊢
	: , : , : , : , : , :
8	instantiation	25	⊢
	: , :
9	instantiation	25	⊢
	: , :
10	instantiation	42, 27, 12	⊢
	: , : , :
11	instantiation	29, 13, 14	⊢
	: , : , :
12	instantiation	42, 34, 15	⊢
	: , : , :
13	instantiation	36, 16	⊢
	: , : , :
14	instantiation	17, 18, 32, 44, 19, 20, 21, 22, 23^*	⊢
	: , : , : , : , : , :
15	instantiation	42, 39, 24	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
17	theorem		⊢
	proveit.numbers.addition.association
18	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	25	⊢
	: , :
21	instantiation	42, 27, 26	⊢
	: , : , :
22	instantiation	42, 27, 28	⊢
	: , : , :
23	instantiation	29, 30, 31	⊢
	: , : , :
24	instantiation	42, 43, 32	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
26	instantiation	42, 34, 33	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
28	instantiation	42, 34, 35	⊢
	: , : , :
29	axiom		⊢
	proveit.logic.equality.equals_transitivity
30	instantiation	36, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.add_6_1
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
33	instantiation	42, 39, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	42, 39, 40	⊢
	: , : , :
36	axiom		⊢
	proveit.logic.equality.substitution
37	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_3
38	instantiation	42, 43, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	42, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
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