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	7	⊢
2	instantiation	7, 4, 5	⊢
	: , : , :
3	instantiation	21, 6	⊢
	: , :
4	instantiation	7, 8, 9	⊢
	: , : , :
5	instantiation	19, 10	⊢
	: , : , :
6	instantiation	11, 45, 12, 13, 14, 15, 31, 27, 29, 25, 16, 17^*	⊢
	: , : , : , : , : , :
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	19, 18	⊢
	: , : , :
9	instantiation	19, 20	⊢
	: , : , :
10	instantiation	21, 22	⊢
	: , :
11	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	instantiation	23	⊢
	: , : , : , :
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	24, 25	⊢
	:
17	instantiation	26, 31	⊢
	:
18	instantiation	28, 27, 31	⊢
	: , :
19	axiom		⊢
	proveit.logic.equality.substitution
20	instantiation	28, 29, 31	⊢
	: , :
21	theorem		⊢
	proveit.logic.equality.equals_reversal
22	instantiation	30, 31	⊢
	:
23	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
24	theorem		⊢
	proveit.numbers.negation.complex_closure
25	instantiation	47, 35, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
27	instantiation	47, 35, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.multiplication.commutation
29	instantiation	47, 35, 34	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.negation.mult_neg_one_right
31	instantiation	47, 35, 36	⊢
	: , : , :
32	instantiation	47, 39, 37	⊢
	: , : , :
33	instantiation	47, 39, 38	⊢
	: , : , :
34	instantiation	47, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
36	assumption		⊢
37	instantiation	47, 43, 41	⊢
	: , : , :
38	instantiation	47, 43, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	47, 43, 44	⊢
	: , : , :
41	instantiation	47, 48, 45	⊢
	: , : , :
42	instantiation	47, 48, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	instantiation	47, 48, 49	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements