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Expression of type Lambda

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, Lambda, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import FALSE, 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 = Lambda(m, Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = FALSE, conditions = [Or(A_1_to_m), 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())
m \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m},(\lnot A_{1}), (\lnot A_{2}), \ldots, (\lnot A_{m})}~\bot \textrm{ if } m \in \mathbb{N}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 25
body: 2
1ExprTuple25
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple25, 10
9Lambdaparameters: 19
body: 11
10Literal
11Conditionalvalue: 12
condition: 13
12Literal
13Operationoperator: 14
operands: 15
14Literal
15ExprTuple16, 17
16Operationoperator: 18
operands: 19
17ExprRangelambda_map: 20
start_index: 24
end_index: 25
18Literal
19ExprTuple21
20Lambdaparameter: 31
body: 22
21ExprRangelambda_map: 23
start_index: 24
end_index: 25
22Operationoperator: 26
operand: 28
23Lambdaparameter: 31
body: 28
24Literal
25Variable
26Literal
27ExprTuple28
28IndexedVarvariable: 29
index: 31
29Variable
30ExprTuple31
31Variable