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Expression of type Forall

from the theory of proveit.numbers.numerals.decimals

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 ExprRange, Variable, a, b, c, d, e, f, g, h, i
from proveit.core_expr_types import Len
from proveit.logic import Equals, Forall
from proveit.numbers import nine, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [a, b, c, d, e, f, g, h, i]
expr = Forall(instance_param_or_params = sub_expr2, instance_expr = Equals(Len(operands = sub_expr2), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, nine)])))
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_{a, b, c, d, e, f, g, h, i}~\left(|\left(a, b, c, d, e, f, g, h, i\right)| = |\left(1, 2, \ldots, 9\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 9
body: 4
4Operationoperator: 5
operands: 6
5Literal
6ExprTuple7, 8
7Operationoperator: 10
operands: 9
8Operationoperator: 10
operands: 11
9ExprTuple12, 13, 14, 15, 16, 17, 18, 19, 20
10Literal
11ExprTuple21
12Variable
13Variable
14Variable
15Variable
16Variable
17Variable
18Variable
19Variable
20Variable
21ExprRangelambda_map: 22
start_index: 23
end_index: 24
22Lambdaparameter: 26
body: 26
23Literal
24Literal
25ExprTuple26
26Variable