Nuprl Lemma : sq_stable__uiff
∀[P,Q:ℙ]. (SqStable(P) ⇒ SqStable(Q) ⇒ SqStable(uiff(P;Q)))
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
sq_stable_wf,
sq_stable__and,
isect_wf,
sq_stable__uimplies
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality,
cumulativity,
sqequalRule,
lambdaEquality,
isect_memberEquality,
independent_functionElimination,
because_Cache
Latex:
\mforall{}[P,Q:\mBbbP{}]. (SqStable(P) {}\mRightarrow{} SqStable(Q) {}\mRightarrow{} SqStable(uiff(P;Q)))
Date html generated:
2019_06_20-AM-11_15_21
Last ObjectModification:
2018_09_26-AM-09_59_32
Theory : core_2
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