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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 Forall, InSet, Not, Or
from proveit.numbers import Natural, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = Not(Or(A_1_to_m)), condition = ExprRange(sub_expr1, Not(IndexedVar(A, sub_expr1)), one, m)), InSet(m, Natural))
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\{\forall_{A_{1}, A_{2}, \ldots, A_{m}~|~(\lnot A_{1}), (\lnot A_{2}), \ldots, (\lnot A_{m})}~(\lnot \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right)) \textrm{ if } m \in \mathbb{N}\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: 3
operand: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple24, 8
7Lambdaparameters: 18
body: 9
8Literal
9Conditionalvalue: 10
condition: 11
10Operationoperator: 25
operand: 15
11Operationoperator: 13
operands: 14
12ExprTuple15
13Literal
14ExprTuple16
15Operationoperator: 17
operands: 18
16ExprRangelambda_map: 19
start_index: 23
end_index: 24
17Literal
18ExprTuple20
19Lambdaparameter: 30
body: 21
20ExprRangelambda_map: 22
start_index: 23
end_index: 24
21Operationoperator: 25
operand: 27
22Lambdaparameter: 30
body: 27
23Literal
24Variable
25Literal
26ExprTuple27
27IndexedVarvariable: 28
index: 30
28Variable
29ExprTuple30
30Variable