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	theorem		⊢
	proveit.logic.equality.equals_reversal
2	instantiation	12, 13, 27, 14, 3, 4, 17, 5, 16, 6^*	⊢
	: , : , : , : , : , :
3	instantiation	20	⊢
	: , :
4	instantiation	20	⊢
	: , :
5	instantiation	37, 22, 7	⊢
	: , : , :
6	instantiation	24, 8, 9	⊢
	: , : , :
7	instantiation	37, 29, 10	⊢
	: , : , :
8	instantiation	31, 11	⊢
	: , : , :
9	instantiation	12, 13, 27, 39, 14, 15, 16, 17, 18^*	⊢
	: , : , : , : , : , :
10	instantiation	37, 34, 19	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
12	theorem		⊢
	proveit.numbers.addition.association
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15	instantiation	20	⊢
	: , :
16	instantiation	37, 22, 21	⊢
	: , : , :
17	instantiation	37, 22, 23	⊢
	: , : , :
18	instantiation	24, 25, 26	⊢
	: , : , :
19	instantiation	37, 38, 27	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21	instantiation	37, 29, 28	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
23	instantiation	37, 29, 30	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	31, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.add_6_1
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
28	instantiation	37, 34, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
30	instantiation	37, 34, 35	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.equality.substitution
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_3
33	instantiation	37, 38, 36	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
35	instantiation	37, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
37	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements