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	⊢
	: , : , :
1	reference	14	⊢
2	instantiation	3, 4, 5, 6	⊢
	: , : , : , :
3	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
4	instantiation	7, 8, 9	⊢
	: , : , :
5	instantiation	10	⊢
	:
6	instantiation	11, 12	⊢
	: , :
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	14, 12	⊢
	: , : , :
9	instantiation	25, 13	⊢
	:
10	axiom		⊢
	proveit.logic.equality.equals_reflexivity
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	14, 15	⊢
	: , : , :
13	instantiation	16, 17, 26	⊢
	: , :
14	axiom		⊢
	proveit.logic.equality.substitution
15	instantiation	18, 19, 31, 20, 21^*	⊢
	: , :
16	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
17	instantiation	48, 36, 22	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.division.div_as_mult
19	instantiation	48, 36, 43	⊢
	: , : , :
20	instantiation	23, 24	⊢
	: , :
21	instantiation	25, 26	⊢
	:
22	instantiation	48, 44, 27	⊢
	: , : , :
23	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
24	instantiation	28, 40, 35, 29	⊢
	: , :
25	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
26	instantiation	30, 31, 32	⊢
	: , :
27	instantiation	48, 46, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
29	instantiation	34, 40, 43, 41	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
31	instantiation	48, 36, 35	⊢
	: , : , :
32	instantiation	48, 36, 37	⊢
	: , : , :
33	instantiation	48, 49, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
35	instantiation	39, 40, 43, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	42, 43	⊢
	:
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
41	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
42	theorem		⊢
	proveit.numbers.negation.real_closure
43	instantiation	48, 44, 45	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	48, 46, 47	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	48, 49, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements