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Expression of type Conditional

from the theory of proveit.logic.booleans.disjunction

In [1]:
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, Conditional, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Not, Or
from proveit.numbers import one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Not(Or(A_1_to_m)), And(ExprRange(sub_expr1, Not(IndexedVar(A, sub_expr1)), one, m)))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{\lnot \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right) \textrm{ if } (\lnot A_{1}) \land  (\lnot A_{2}) \land  \ldots \land  (\lnot A_{m})\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 16
operand: 6
2Operationoperator: 4
operands: 5
3ExprTuple6
4Literal
5ExprTuple7
6Operationoperator: 8
operands: 9
7ExprRangelambda_map: 10
start_index: 14
end_index: 15
8Literal
9ExprTuple11
10Lambdaparameter: 21
body: 12
11ExprRangelambda_map: 13
start_index: 14
end_index: 15
12Operationoperator: 16
operand: 18
13Lambdaparameter: 21
body: 18
14Literal
15Variable
16Literal
17ExprTuple18
18IndexedVarvariable: 19
index: 21
19Variable
20ExprTuple21
21Variable