Nuprl Lemma : squash_elim
∀[P:ℙ]. (SqStable(P) ⇒ (↓P ⇐⇒ P))
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
squash: ↓T,
implies: P ⇒ Q
Definitions unfolded in proof :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
squash: ↓T
Lemmas referenced :
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
imageMemberEquality,
baseClosed,
functionEquality,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[P:\mBbbP{}]. (SqStable(P) {}\mRightarrow{} (\mdownarrow{}P \mLeftarrow{}{}\mRightarrow{} P))
Date html generated:
2019_06_20-AM-11_15_47
Last ObjectModification:
2018_09_26-AM-10_23_47
Theory : core_2
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