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Expression of type ExprTuple

from the theory of proveit.logic.booleans.quantification

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, ExprTuple, Lambda
from proveit.core_expr_types import P__x_1_to_m_y_1_to_n, Q__x_1_to_m, R__x_1_to_m_y_1_to_n, x_1_to_m, y_1_to_n
from proveit.logic import Forall
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x_1_to_m], Conditional(Forall(instance_param_or_params = [y_1_to_n], instance_expr = P__x_1_to_m_y_1_to_n, condition = R__x_1_to_m_y_1_to_n), Q__x_1_to_m)))
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(x_{1}, x_{2}, \ldots, x_{m}\right) \mapsto \left\{\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~R\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } Q\left(x_{1}, x_{2}, \ldots, x_{m}\right)\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: 8
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Variable
8ExprTuple17
9Lambdaparameters: 10
body: 11
10ExprTuple18
11Conditionalvalue: 12
condition: 13
12Operationoperator: 14
operands: 16
13Operationoperator: 15
operands: 16
14Variable
15Variable
16ExprTuple17, 18
17ExprRangelambda_map: 19
start_index: 22
end_index: 20
18ExprRangelambda_map: 21
start_index: 22
end_index: 23
19Lambdaparameter: 29
body: 24
20Variable
21Lambdaparameter: 29
body: 25
22Literal
23Variable
24IndexedVarvariable: 26
index: 29
25IndexedVarvariable: 27
index: 29
26Variable
27Variable
28ExprTuple29
29Variable