Nuprl Lemma : fun-connected_weakening
∀[T:Type]. ∀f:T ⟶ T. ∀x,y:T. (y = f+(x) ⇒ y is f*(x))
Proof
Definitions occuring in Statement :
strict-fun-connected: y = f+(x),
fun-connected: y is f*(x),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
strict-fun-connected: y = f+(x),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ
Lemmas referenced :
and_wf,
not_wf,
equal_wf,
fun-connected_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}f:T {}\mrightarrow{} T. \mforall{}x,y:T. (y = f+(x) {}\mRightarrow{} y is f*(x))
Date html generated:
2016_05_15-PM-05_02_53
Last ObjectModification:
2015_12_27-PM-02_29_43
Theory : general
Home
Index