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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5, 20, 6, 21, 10, 31, 11, 12	, , ⊢
	: , : , : , :
3	instantiation	7, 20, 38, 21, 8, 9, 10, 31, 11, 12, 13^*	, , ⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.addition.elim_zero_any
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
6	instantiation	14	⊢
	: , : , : , :
7	theorem		⊢
	proveit.numbers.addition.association
8	instantiation	26	⊢
	: , :
9	instantiation	26	⊢
	: , :
10	instantiation	15, 23, 31	⊢
	: , :
11	assumption		⊢
12	assumption		⊢
13	instantiation	16, 17, 18^*	⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
15	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
16	theorem		⊢
	proveit.logic.equality.equals_reversal
17	instantiation	19, 20, 38, 41, 21, 22, 23, 24, 31, 25^*	⊢
	: , : , : , : , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
19	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
20	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
21	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22	instantiation	26	⊢
	: , :
23	instantiation	39, 28, 27	⊢
	: , : , :
24	instantiation	39, 28, 29	⊢
	: , : , :
25	instantiation	30, 31	⊢
	:
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27	instantiation	39, 33, 32	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
29	instantiation	39, 33, 34	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
31	assumption		⊢
32	instantiation	39, 36, 35	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
34	instantiation	39, 36, 37	⊢
	: , : , :
35	instantiation	39, 40, 38	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
37	instantiation	39, 40, 41	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
39	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements