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, 4, 5^*	⊢
	: , : , : , :
1	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
2	instantiation	53, 54, 6	⊢
	: , : , :
3	reference	51	⊢
4	reference	49	⊢
5	instantiation	18, 7, 8	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
7	instantiation	24, 52, 9, 10, 11, 12	⊢
	: , : , : , :
8	instantiation	13, 14, 15, 34, 16^, 17^	⊢
	: , : , :
9	instantiation	32	⊢
	: , :
10	instantiation	32	⊢
	: , :
11	instantiation	18, 19, 20	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.mult_6_2
13	theorem		⊢
	proveit.numbers.division.frac_cancel_left
14	instantiation	53, 22, 21	⊢
	: , : , :
15	instantiation	53, 22, 23	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
17	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_3
18	axiom		⊢
	proveit.logic.equality.equals_transitivity
19	instantiation	24, 52, 25, 26, 27, 28	⊢
	: , : , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_6
21	instantiation	53, 30, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
23	instantiation	53, 30, 31	⊢
	: , : , :
24	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
25	instantiation	32	⊢
	: , :
26	instantiation	32	⊢
	: , :
27	instantiation	33, 34	⊢
	:
28	instantiation	35, 36	⊢
	:
29	instantiation	53, 38, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31	instantiation	53, 38, 39	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
34	instantiation	53, 41, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
36	instantiation	53, 41, 42	⊢
	: , : , :
37	instantiation	53, 44, 43	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
39	instantiation	53, 44, 45	⊢
	: , : , :
40	instantiation	53, 47, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	53, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
46	instantiation	53, 50, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	53, 50, 51	⊢
	: , : , :
49	instantiation	53, 54, 52	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	53, 54, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
^*equality replacement requirements