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Expression of type ExprTuple

from the theory of proveit.logic.booleans.conjunction

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, ExprTuple, IndexedVar, Lambda, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, 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 = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = And(A_1_to_m), condition = Not(Or(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(m \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}~|~\lnot \left((\lnot A_{1}) \lor  (\lnot A_{2}) \lor  \ldots \lor  (\lnot A_{m})\right)}~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{m}\right) \textrm{ if } m \in \mathbb{N}\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 26
body: 3
2ExprTuple26
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple26, 11
10Lambdaparameters: 16
body: 12
11Literal
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operands: 16
14Operationoperator: 28
operand: 19
15Literal
16ExprTuple18
17ExprTuple19
18ExprRangelambda_map: 20
start_index: 25
end_index: 26
19Operationoperator: 21
operands: 22
20Lambdaparameter: 33
body: 30
21Literal
22ExprTuple23
23ExprRangelambda_map: 24
start_index: 25
end_index: 26
24Lambdaparameter: 33
body: 27
25Literal
26Variable
27Operationoperator: 28
operand: 30
28Literal
29ExprTuple30
30IndexedVarvariable: 31
index: 33
31Variable
32ExprTuple33
33Variable