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	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 13	⊢
	:
4	axiom		⊢
	proveit.logic.equality.equals_transitivity
5	instantiation	8, 9	⊢
	: , : , :
6	instantiation	10, 11, 12, 13, 14^*	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.division.frac_one_denom
8	axiom		⊢
	proveit.logic.equality.substitution
9	instantiation	15, 16, 55, 17, 18, 19, 27, 24, 25	⊢
	: , : , : , : , : , :
10	theorem		⊢
	proveit.numbers.division.frac_cancel_left
11	instantiation	53, 21, 20	⊢
	: , : , :
12	instantiation	53, 21, 22	⊢
	: , : , :
13	instantiation	23, 24, 25	⊢
	: , :
14	instantiation	26, 27	⊢
	:
15	theorem		⊢
	proveit.numbers.multiplication.association
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	instantiation	28	⊢
	: , :
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	53, 30, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
22	instantiation	53, 30, 31	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
24	instantiation	53, 51, 32	⊢
	: , : , :
25	instantiation	53, 51, 33	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
27	instantiation	53, 51, 34	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	instantiation	53, 36, 35	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31	instantiation	53, 36, 37	⊢
	: , : , :
32	instantiation	53, 38, 39	⊢
	: , : , :
33	instantiation	53, 40, 41	⊢
	: , : , :
34	instantiation	53, 42, 43	⊢
	: , : , :
35	instantiation	53, 45, 44	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37	instantiation	53, 45, 46	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
41	instantiation	47, 48	⊢
	:
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	53, 49, 50	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
47	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
48	instantiation	53, 51, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	53, 54, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
52	assumption		⊢
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.nat2
^*equality replacement requirements