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	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
2	instantiation	4, 26, 8, 5, 6^*	⊢
	: , :
3	instantiation	7, 8, 41, 9	⊢
	: , :
4	theorem		⊢
	proveit.numbers.rounding.floor_increasing_less_eq
5	instantiation	10, 34, 26, 18, 11, 12, 13^*	⊢
	: , : , :
6	instantiation	14, 15	⊢
	:
7	theorem		⊢
	proveit.numbers.rounding.floor_of_real_below_int
8	instantiation	16, 34, 18	⊢
	: , :
9	instantiation	17, 34, 18, 27, 19, 23, 20^*	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
11	instantiation	21, 26, 27, 28	⊢
	: , : , :
12	instantiation	22, 23	⊢
	: , :
13	instantiation	24, 30	⊢
	:
14	theorem		⊢
	proveit.numbers.rounding.floor_of_integer
15	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
16	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
17	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
18	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
19	instantiation	25, 26, 27, 28	⊢
	: , : , :
20	instantiation	29, 30	⊢
	:
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
22	theorem		⊢
	proveit.numbers.ordering.relax_less
23	instantiation	31, 44	⊢
	:
24	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
27	instantiation	42, 36, 32	⊢
	: , : , :
28	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
29	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
30	instantiation	42, 33, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
32	instantiation	42, 40, 35	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	42, 36, 37	⊢
	: , : , :
35	instantiation	42, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	42, 40, 41	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	42, 43, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
44	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
^*equality replacement requirements