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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 Function, f, i, j
from proveit.core_expr_types import f_i_to_j
from proveit.logic import Equals, Forall
from proveit.numbers import Add, one, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Add(i, two)
expr = Forall(instance_param_or_params = [f, i, j], instance_expr = Equals([f_i_to_j], [Function(f, [i]), Function(f, [Add(i, one)]), Function(f, [sub_expr1])]), condition = Equals(j, sub_expr1))
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_{f, i, j~|~j = \left(i + 2\right)}~\left(\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) = \left(f\left(i\right), f\left(i + 1\right), f\left(i + 2\right)\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: 4
body: 5
4ExprTuple25, 32, 18
5Conditionalvalue: 6
condition: 7
6Operationoperator: 9
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple18, 24
11ExprTuple13
12ExprTuple14, 15, 16
13ExprRangelambda_map: 17
start_index: 32
end_index: 18
14Operationoperator: 25
operand: 32
15Operationoperator: 25
operand: 23
16Operationoperator: 25
operand: 24
17Lambdaparameter: 30
body: 22
18Variable
19ExprTuple32
20ExprTuple23
21ExprTuple24
22Operationoperator: 25
operand: 30
23Operationoperator: 28
operands: 27
24Operationoperator: 28
operands: 29
25Variable
26ExprTuple30
27ExprTuple32, 31
28Literal
29ExprTuple32, 33
30Variable
31Literal
32Variable
33Literal