Nuprl Lemma : squash_and
∀[a,b:ℙ]. uiff(↓a ∧ b;(↓a) ∧ (↓b))
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T,
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
cand: A c∧ B
Lemmas referenced :
and_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
hypothesis,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
baseClosed,
independent_pairEquality,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[a,b:\mBbbP{}]. uiff(\mdownarrow{}a \mwedge{} b;(\mdownarrow{}a) \mwedge{} (\mdownarrow{}b))
Date html generated:
2016_05_13-PM-03_13_55
Last ObjectModification:
2016_01_06-PM-05_49_43
Theory : core_2
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