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Expression of type Implies

from the theory of proveit.logic.sets.inclusion

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 A, B, Px, Py, x, y
from proveit.logic import Forall, Implies
In [2]:
# build up the expression from sub-expressions
expr = Implies(Forall(instance_param_or_params = [x], instance_expr = Px, domain = A), Forall(instance_param_or_params = [y], instance_expr = Py, domain = B))
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[\forall_{x \in A}~P\left(x\right)\right] \Rightarrow \left[\forall_{y \in B}~P\left(y\right)\right]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operand: 8
4Operationoperator: 6
operand: 9
5ExprTuple8
6Literal
7ExprTuple9
8Lambdaparameter: 22
body: 10
9Lambdaparameter: 24
body: 11
10Conditionalvalue: 12
condition: 13
11Conditionalvalue: 14
condition: 15
12Operationoperator: 18
operand: 22
13Operationoperator: 20
operands: 17
14Operationoperator: 18
operand: 24
15Operationoperator: 20
operands: 21
16ExprTuple22
17ExprTuple22, 23
18Variable
19ExprTuple24
20Literal
21ExprTuple24, 25
22Variable
23Variable
24Variable
25Variable