Nuprl Lemma : rel_plus_functionality_wrt_rel_implies
∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ]. (R1 => R2 ⇒ R1+ => R2+)
Proof
Definitions occuring in Statement :
rel_plus: R+,
rel_implies: R1 => R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
rel_plus: R+,
rel_implies: R1 => R2,
infix_ap: x f y,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
rel_exp_wf,
exists_wf,
nat_plus_wf,
nat_plus_subtype_nat,
all_wf,
rel_exp_monotone
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
cut,
dependent_functionElimination,
hypothesis,
independent_functionElimination,
applyEquality,
lemma_by_obid,
isectElimination,
because_Cache,
lambdaEquality,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R1,R2:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (R1 => R2 {}\mRightarrow{} R1\msupplus{} => R2\msupplus{})
Date html generated:
2016_05_14-PM-03_54_01
Last ObjectModification:
2015_12_26-PM-06_56_15
Theory : relations2
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