Nuprl Lemma : iseg-l-ordered
∀[T:Type]. ∀R:T ⟶ T ⟶ ℙ. ∀a,b:T List. (a ≤ b ⇒ l-ordered(T;x,y.R[x;y];b) ⇒ l-ordered(T;x,y.R[x;y];a))
Proof
Definitions occuring in Statement :
l-ordered: l-ordered(T;x,y.R[x; y];L),
iseg: l1 ≤ l2,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
l-ordered-is-sorted-by,
iseg-sorted-by,
l-ordered_wf,
iseg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
productElimination,
independent_functionElimination,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}. \mforall{}a,b:T List. (a \mleq{} b {}\mRightarrow{} l-ordered(T;x,y.R[x;y];b) {}\mRightarrow{} l-ordered(T;x,y.R[x;y];a))
Date html generated:
2016_05_15-PM-04_39_16
Last ObjectModification:
2015_12_27-PM-02_41_44
Theory : general
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