Nuprl Lemma : monotone_wf
∀[T,T':Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[R':T' ⟶ T' ⟶ ℙ]. ∀[f:T ⟶ T']. (monotone(T;T';x,y.R[x;y];x,y.R'[x;y];f) ∈ ℙ)
Proof
Definitions occuring in Statement :
monotone: monotone(T;T';x,y.R[x; y];x,y.R'[x; y];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 :
monotone: monotone(T;T';x,y.R[x; y];x,y.R'[x; y];f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[T,T':Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[R':T' {}\mrightarrow{} T' {}\mrightarrow{} \mBbbP{}]. \mforall{}[f:T {}\mrightarrow{} T'].
(monotone(T;T';x,y.R[x;y];x,y.R'[x;y];f) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_03_07
Last ObjectModification:
2015_12_26-PM-11_25_09
Theory : gen_algebra_1
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