Nuprl Lemma : squash_functionality_wrt_iff
∀[P,Q:ℙ]. ({P ⇐⇒ Q} ⇒ {↓P ⇐⇒ ↓Q})
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
squash: ↓T,
implies: P ⇒ Q
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q,
guard: {T},
squash: ↓T
Lemmas referenced :
iff_wf,
squash_wf,
squash_functionality_wrt_implies
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
Error :inhabitedIsType,
because_Cache,
universeEquality,
Error :universeIsType,
lambdaFormation,
productElimination,
independent_functionElimination,
sqequalRule,
Error :isect_memberFormation_alt,
independent_pairFormation,
lambdaEquality,
dependent_functionElimination,
independent_pairEquality,
imageElimination,
imageMemberEquality,
baseClosed,
isect_memberEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. (\{P \mLeftarrow{}{}\mRightarrow{} Q\} {}\mRightarrow{} \{\mdownarrow{}P \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}Q\})
Date html generated:
2019_06_20-AM-11_17_40
Last ObjectModification:
2018_09_26-AM-10_25_00
Theory : core_2
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