Nuprl Lemma : sq_stable__anti_sym
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. SqStable(AntiSym(T;x,y.R[x;y]))
Proof
Definitions occuring in Statement :
anti_sym: AntiSym(T;x,y.R[x; y]),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
anti_sym: AntiSym(T;x,y.R[x; y]),
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],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
sq_stable: SqStable(P)
Lemmas referenced :
sq_stable__all,
all_wf,
equal_wf,
sq_stable__equal,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
cumulativity,
functionEquality,
applyEquality,
functionExtensionality,
hypothesis,
independent_functionElimination,
lambdaFormation,
because_Cache,
universeEquality,
dependent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. SqStable(AntiSym(T;x,y.R[x;y]))
Date html generated:
2016_10_21-AM-09_42_43
Last ObjectModification:
2016_08_01-PM-09_48_52
Theory : rel_1
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