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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 Conditional, Lambda, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Boolean, Forall, InSet, Or
from proveit.numbers import NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = InSet(Or(A_1_to_m), Boolean), domain = Boolean), InSet(m, NaturalPos)))
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} \in \mathbb{B}}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right) \in \mathbb{B}\right) \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: 8
4Operationoperator: 26
operands: 7
5Literal
6ExprTuple8
7ExprTuple25, 9
8Lambdaparameters: 19
body: 10
9Literal
10Conditionalvalue: 11
condition: 12
11Operationoperator: 26
operands: 13
12Operationoperator: 14
operands: 15
13ExprTuple16, 29
14Literal
15ExprTuple17
16Operationoperator: 18
operands: 19
17ExprRangelambda_map: 20
start_index: 24
end_index: 25
18Literal
19ExprTuple21
20Lambdaparameter: 32
body: 22
21ExprRangelambda_map: 23
start_index: 24
end_index: 25
22Operationoperator: 26
operands: 27
23Lambdaparameter: 32
body: 28
24Literal
25Variable
26Literal
27ExprTuple28, 29
28IndexedVarvariable: 30
index: 32
29Literal
30Variable
31ExprTuple32
32Variable