Nuprl Lemma : rel_implies_functionality
∀[T:Type]. ∀[A1,A2,B1,B2:T ⟶ T ⟶ ℙ]. (A1 ⇐ A2 ⇒ B1 => B2 ⇒ {A1 => B1 ⇒ A2 => B2})
Proof
Definitions occuring in Statement :
rel_rev_implies: R1 ⇐ R2,
rel_implies: R1 => R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
rel_implies: R1 => R2,
guard: {T},
rel_rev_implies: R1 ⇐ R2,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
infix_ap: x f y,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
applyEquality,
hypothesisEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
functionEquality,
hypothesis,
cumulativity,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[A1,A2,B1,B2:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (A1 \mLeftarrow{}{} A2 {}\mRightarrow{} B1 => B2 {}\mRightarrow{} \{A1 => B1 {}\mRightarrow{} A2 => B2\})
Date html generated:
2016_05_14-AM-06_04_50
Last ObjectModification:
2015_12_26-AM-11_33_04
Theory : relations
Home
Index