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	⊢
	: , : , :
3	instantiation	7, 6	⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	7, 8	⊢
	: , :
6	instantiation	9, 10, 11, 41, 12, 13, 14, 15, 23, 16, 25, 17^*	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.logic.equality.equals_reversal
8	instantiation	18, 25	⊢
	:
9	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	instantiation	19	⊢
	: , : , : , :
14	instantiation	39, 29, 20	⊢
	: , : , :
15	instantiation	39, 29, 21	⊢
	: , : , :
16	instantiation	22, 23	⊢
	:
17	instantiation	24, 25	⊢
	:
18	theorem		⊢
	proveit.numbers.negation.mult_neg_one_left
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
20	instantiation	39, 33, 26	⊢
	: , : , :
21	instantiation	39, 33, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.negation.complex_closure
23	instantiation	39, 29, 28	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
25	instantiation	39, 29, 30	⊢
	: , : , :
26	instantiation	39, 37, 31	⊢
	: , : , :
27	instantiation	39, 37, 32	⊢
	: , : , :
28	instantiation	39, 33, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	assumption		⊢
31	instantiation	39, 40, 35	⊢
	: , : , :
32	instantiation	39, 40, 36	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
34	instantiation	39, 37, 38	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
38	instantiation	39, 40, 41	⊢
	: , : , :
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