Expression of type Conditional ¶

from the theory of proveit.logic.booleans.disjunction ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, B, Conditional, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m, B_1_to_m
from proveit.logic import Boolean, Forall, Implies, InSet, Not, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(B, sub_expr1)
sub_expr3 = IndexedVar(A, sub_expr1)
expr = Conditional(Forall(instance_param_or_params = [A_1_to_m, B_1_to_m], instance_expr = Or(ExprRange(sub_expr1, Not(sub_expr2), one, m)), domain = Boolean, conditions = [Or(ExprRange(sub_expr1, Not(sub_expr3), one, m)), ExprRange(sub_expr1, Implies(sub_expr3, sub_expr2), one, m)]), InSet(m, Natural))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, B_{1}, B_{2}, \ldots, B_{m} \in \mathbb{B}~|~(\lnot A_{1}) \lor  (\lnot A_{2}) \lor  \ldots \lor  (\lnot A_{m}),\left(A_{1} \Rightarrow B_{1}\right), \left(A_{2} \Rightarrow B_{2}\right), \ldots, \left(A_{m} \Rightarrow B_{m}\right)}~\left((\lnot B_{1}) \lor  (\lnot B_{2}) \lor  \ldots \lor  (\lnot B_{m})\right) \textrm{ if } m \in \mathbb{N}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 37 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	41, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	10, 11
9	Conditional	value: 12 condition: 13
10	ExprRange	lambda_map: 14 start_index: 40 end_index: 41
11	ExprRange	lambda_map: 15 start_index: 40 end_index: 41
12	Operation	operator: 27 operands: 16
13	Operation	operator: 17 operands: 18
14	Lambda	parameter: 53 body: 50
15	Lambda	parameter: 53 body: 46
16	ExprTuple	19
17	Literal
18	ExprTuple	20, 21, 22, 23
19	ExprRange	lambda_map: 24 start_index: 40 end_index: 41
20	ExprRange	lambda_map: 25 start_index: 40 end_index: 41
21	ExprRange	lambda_map: 26 start_index: 40 end_index: 41
22	Operation	operator: 27 operands: 28
23	ExprRange	lambda_map: 29 start_index: 40 end_index: 41
24	Lambda	parameter: 53 body: 30
25	Lambda	parameter: 53 body: 31
26	Lambda	parameter: 53 body: 32
27	Literal
28	ExprTuple	33
29	Lambda	parameter: 53 body: 34
30	Operation	operator: 47 operand: 46
31	Operation	operator: 37 operands: 36
32	Operation	operator: 37 operands: 38
33	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
34	Operation	operator: 42 operands: 43
35	ExprTuple	46
36	ExprTuple	50, 44
37	Literal
38	ExprTuple	46, 44
39	Lambda	parameter: 53 body: 45
40	Literal
41	Variable
42	Literal
43	ExprTuple	50, 46
44	Literal
45	Operation	operator: 47 operand: 50
46	IndexedVar	variable: 49 index: 53
47	Literal
48	ExprTuple	50
49	Variable
50	IndexedVar	variable: 51 index: 53
51	Variable
52	ExprTuple	53
53	Variable

Expression of type Conditional¶

from the theory of proveit.logic.booleans.disjunction¶

Expression of type Conditional ¶

from the theory of proveit.logic.booleans.disjunction ¶