Nuprl Lemma : rel_plus_minimal
∀[T:Type]. ∀[R,Q:T ⟶ T ⟶ ℙ]. (R => Q ⇒ Trans(T;x,y.x Q y) ⇒ R+ => Q)
Proof
Definitions occuring in Statement :
rel_plus: R+,
rel_implies: R1 => R2,
trans: Trans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
infix_ap: x f y,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
so_apply: x[s1;s2],
infix_ap: x f y,
all: ∀x:A. B[x],
prop: ℙ,
rel_implies: R1 => R2,
so_lambda: λ2x y.t[x; y],
guard: {T}
Lemmas referenced :
rel_plus_closure,
rel_plus_wf,
trans_wf,
rel_implies_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
independent_functionElimination,
sqequalRule,
applyEquality,
because_Cache,
lambdaEquality,
functionEquality,
cumulativity,
universeEquality,
dependent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[R,Q:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (R => Q {}\mRightarrow{} Trans(T;x,y.x Q y) {}\mRightarrow{} R\msupplus{} => Q)
Date html generated:
2016_05_14-PM-03_55_13
Last ObjectModification:
2015_12_26-PM-06_55_43
Theory : relations2
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