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