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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 C, Conditional, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, D_1_to_n
from proveit.logic import And, Forall, InSet, Or
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C, D_1_to_n], instance_expr = Or(A_1_to_l, C, B_1_to_m, D_1_to_n), condition = Or(A_1_to_l, B_1_to_m, C, D_1_to_n)), And(InSet(l, Natural), InSet(m, Natural), InSet(n, 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_{l}, B_{1}, B_{2}, \ldots, B_{m}, C, D_{1}, D_{2}, \ldots, D_{n}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l}\lor B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m} \lor C\lor D_{1} \lor  D_{2} \lor  \ldots \lor  D_{n}}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l} \lor C\lor B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\lor D_{1} \lor  D_{2} \lor  \ldots \lor  D_{n}\right) \textrm{ if } l \in \mathbb{N} ,  m \in \mathbb{N} ,  n \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
6ExprTuple8, 9, 10
7Lambdaparameters: 21
body: 11
8Operationoperator: 14
operands: 12
9Operationoperator: 14
operands: 13
10Operationoperator: 14
operands: 15
11Conditionalvalue: 16
condition: 17
12ExprTuple27, 18
13ExprTuple29, 18
14Literal
15ExprTuple32, 18
16Operationoperator: 20
operands: 19
17Operationoperator: 20
operands: 21
18Literal
19ExprTuple22, 24, 23, 25
20Literal
21ExprTuple22, 23, 24, 25
22ExprRangelambda_map: 26
start_index: 31
end_index: 27
23ExprRangelambda_map: 28
start_index: 31
end_index: 29
24Variable
25ExprRangelambda_map: 30
start_index: 31
end_index: 32
26Lambdaparameter: 40
body: 33
27Variable
28Lambdaparameter: 40
body: 34
29Variable
30Lambdaparameter: 40
body: 35
31Literal
32Variable
33IndexedVarvariable: 36
index: 40
34IndexedVarvariable: 37
index: 40
35IndexedVarvariable: 38
index: 40
36Variable
37Variable
38Variable
39ExprTuple40
40Variable