Nuprl Lemma : fun-connected-test
∀[T:Type]. ∀f:T ⟶ T. ∀x,y,z,w:T. (y is f*(x) ⇒ z is f*(y) ⇒ w is f*(z) ⇒ w is f*(x))
Proof
Definitions occuring in Statement :
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 :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
guard: {T},
prop: ℙ
Lemmas referenced :
fun-connected_transitivity,
fun-connected_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}f:T {}\mrightarrow{} T. \mforall{}x,y,z,w:T. (y is f*(x) {}\mRightarrow{} z is f*(y) {}\mRightarrow{} w is f*(z) {}\mRightarrow{} w is f*(x))
Date html generated:
2016_05_15-PM-05_04_00
Last ObjectModification:
2015_12_27-PM-02_28_23
Theory : general
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