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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 Conditional, ExprRange, ExprTuple, Function, Lambda, P, Pk, Variable, i, j, k
from proveit.logic import And, Forall, Implies, InSet
from proveit.numbers import Add, Integer, Interval, LessEq, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([i, j], Conditional(Forall(instance_param_or_params = [P], instance_expr = Implies(Forall(instance_param_or_params = [k], instance_expr = Pk, domain = Interval(i, j)), And(ExprRange(sub_expr1, Function(P, [sub_expr1]), i, j))), condition = LessEq(i, Add(j, one))), And(InSet(i, Integer), InSet(j, Integer)))))
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(\left(i, j\right) \mapsto \left\{\forall_{P~|~i \leq \left(j + 1\right)}~\left(\left[\forall_{k \in \{i~\ldotp \ldotp~j\}}~P\left(k\right)\right] \Rightarrow \left(P\left(i\right) \land  P\left(i + 1\right) \land  \ldots \land  P\left(j\right)\right)\right) \textrm{ if } i \in \mathbb{Z} ,  j \in \mathbb{Z}\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
1Lambdaparameters: 47
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 24
operand: 7
4Operationoperator: 26
operands: 6
5ExprTuple7
6ExprTuple8, 9
7Lambdaparameter: 41
body: 11
8Operationoperator: 39
operands: 12
9Operationoperator: 39
operands: 13
10ExprTuple41
11Conditionalvalue: 14
condition: 15
12ExprTuple48, 16
13ExprTuple49, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16Literal
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple48, 23
21Operationoperator: 24
operand: 30
22Operationoperator: 26
operands: 27
23Operationoperator: 28
operands: 29
24Literal
25ExprTuple30
26Literal
27ExprTuple31
28Literal
29ExprTuple49, 32
30Lambdaparameter: 43
body: 33
31ExprRangelambda_map: 34
start_index: 48
end_index: 49
32Literal
33Conditionalvalue: 35
condition: 36
34Lambdaparameter: 45
body: 37
35Operationoperator: 41
operand: 43
36Operationoperator: 39
operands: 40
37Operationoperator: 41
operand: 45
38ExprTuple43
39Literal
40ExprTuple43, 44
41Variable
42ExprTuple45
43Variable
44Operationoperator: 46
operands: 47
45Variable
46Literal
47ExprTuple48, 49
48Variable
49Variable