Nuprl Lemma : sq_stable__and
∀[P:ℙ]. ∀[Q:⋂p:P. ℙ]. (SqStable(P) ⇒ (P ⇒ SqStable(Q)) ⇒ SqStable(P ∧ Q))
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
and: P ∧ Q,
isect: ⋂x:A. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
sq_stable: SqStable(P),
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
squash: ↓T,
cand: A c∧ B
Lemmas referenced :
sq_stable_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
cumulativity,
hypothesisEquality,
hypothesis,
rename,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
functionEquality,
applyEquality,
lambdaEquality,
isectEquality,
universeEquality,
independent_functionElimination,
imageElimination,
introduction,
productElimination,
imageMemberEquality,
baseClosed,
independent_pairFormation
Latex:
\mforall{}[P:\mBbbP{}]. \mforall{}[Q:\mcap{}p:P. \mBbbP{}]. (SqStable(P) {}\mRightarrow{} (P {}\mRightarrow{} SqStable(Q)) {}\mRightarrow{} SqStable(P \mwedge{} Q))
Date html generated:
2016_05_13-PM-03_09_40
Last ObjectModification:
2016_01_06-PM-05_49_10
Theory : core_2
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