Nuprl Lemma : uimplies-iff-squash-implies
∀[P,Q:ℙ]. (Q supposing P ⇐⇒ (↓P) ⇒ Q)
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
squash: ↓T,
implies: P ⇒ Q
Definitions unfolded in proof :
squash: ↓T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q
Lemmas referenced :
isect_wf,
image-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
baseClosed,
hypothesis,
lambdaEquality,
functionEquality,
universeEquality,
imageElimination,
rename,
introduction,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
imageMemberEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. (Q supposing P \mLeftarrow{}{}\mRightarrow{} (\mdownarrow{}P) {}\mRightarrow{} Q)
Date html generated:
2016_05_13-PM-03_07_33
Last ObjectModification:
2016_01_06-PM-05_28_21
Theory : core_2
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