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Expression of type Forall

from the theory of proveit.core_expr_types.conditionals

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, Q, a, n
from proveit.core_expr_types import R_1_to_n
from proveit.logic import And, Equals, Forall
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [a, Q, R_1_to_n], instance_expr = Equals(Conditional(a, And(Q, And(R_1_to_n))), Conditional(a, And(Q, R_1_to_n))).with_wrapping_at(1)), domain = 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())
\forall_{n \in \mathbb{N}}~\left[\forall_{a, Q, R_{1}, R_{2}, \ldots, R_{n}}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q ,  R_{1} \land  R_{2} \land  \ldots \land  R_{n}\right.. \\  = \left\{a \textrm{ if } Q, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \end{array} \end{array}\right)\right]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 31
body: 4
3ExprTuple31
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple31, 12
11Lambdaparameters: 13
body: 14
12Literal
13ExprTuple20, 25, 28
14Operationoperator: 15
operands: 16
15Literal
16ExprTuple17, 18
17Conditionalvalue: 20
condition: 19
18Conditionalvalue: 20
condition: 21
19Operationoperator: 26
operands: 22
20Variable
21Operationoperator: 26
operands: 23
22ExprTuple25, 24
23ExprTuple25, 28
24Operationoperator: 26
operands: 27
25Variable
26Literal
27ExprTuple28
28ExprRangelambda_map: 29
start_index: 30
end_index: 31
29Lambdaparameter: 35
body: 32
30Literal
31Variable
32IndexedVarvariable: 33
index: 35
33Variable
34ExprTuple35
35Variable