Nuprl Lemma : rel_exp_functionality_wrt_rel_implies
∀n:ℕ. ∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ]. (R1 => R2 ⇒ R1^n => R2^n)
Proof
Definitions occuring in Statement :
rel_implies: R1 => R2,
rel_exp: R^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Lemmas referenced :
rel_exp_monotone
Rules used in proof :
cut,
lemma_by_obid,
hypothesis
Latex:
\mforall{}n:\mBbbN{}. \mforall{}[T:Type]. \mforall{}[R1,R2:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (R1 => R2 {}\mRightarrow{} rel\_exp(T; R1; n) => rel\_exp(T; R2; n))
Date html generated:
2016_05_14-PM-03_54_34
Last ObjectModification:
2015_12_26-PM-06_56_10
Theory : relations2
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