Nuprl Lemma : order-preserving_wf
∀[A,B:Type]. ∀[R1:A ⟶ A ⟶ ℙ]. ∀[R2:B ⟶ B ⟶ ℙ]. ∀[f:A ⟶ B].
(order-preserving(A;B;a1,a2.R1[a1;a2];b1,b2.R2[b1;b2];f) ∈ ℙ)
Proof
Definitions occuring in Statement :
order-preserving: order-preserving(A;B;a1,a2.R1[a1; a2];b1,b2.R2[b1; b2];f),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
order-preserving: order-preserving(A;B;a1,a2.R1[a1; a2];b1,b2.R2[b1; b2];f),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s]
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[R1:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. \mforall{}[R2:B {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}]. \mforall{}[f:A {}\mrightarrow{} B].
(order-preserving(A;B;a1,a2.R1[a1;a2];b1,b2.R2[b1;b2];f) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-03_28_32
Last ObjectModification:
2015_12_27-PM-01_09_25
Theory : general
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