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	axiom		⊢
	proveit.logic.booleans.negation.not_f
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	6, 7	⊢
	:
6	axiom		⊢
	proveit.logic.booleans.negation.negation_elim
7	instantiation	8, 9	⊢
	: , :
8	theorem		⊢
	proveit.logic.equality.unfold_not_equals
9	instantiation	10, 11	⊢
	: , :
10	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
11	instantiation	12, 41, 13, 14	⊢
	: , :
12	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
13	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
14	instantiation	15, 34, 16, 17, 18, 19^, 20^	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
17	instantiation	39, 35, 21	⊢
	: , : , :
18	instantiation	22, 23	⊢
	:
19	instantiation	24, 25, 26	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
21	instantiation	39, 37, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
24	theorem		⊢
	proveit.logic.equality.sub_right_side_into
25	instantiation	28, 30	⊢
	:
26	instantiation	29, 30, 31	⊢
	: , :
27	instantiation	39, 40, 32	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.elim_zero_right
29	theorem		⊢
	proveit.numbers.addition.commutation
30	instantiation	39, 33, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	39, 35, 36	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	39, 37, 38	⊢
	: , : , :
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