Nuprl Lemma : p-and_wf
∀[A,B:PType]. (p-and(A;B) ∈ PType)
Proof
Definitions occuring in Statement :
p-and: p-and(A;B),
p-type: PType,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
p-type: PType,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
iff: P ⇐⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
uimplies: b supposing a,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
p-and: p-and(A;B)
Lemmas referenced :
p-type_wf,
quotient-member-eq,
iff_wf,
equiv_rel_iff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
extract_by_obid,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
thin,
instantiate,
isectElimination,
universeEquality,
lambdaEquality_alt,
hypothesisEquality,
applyEquality,
cumulativity,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
dependent_functionElimination,
productEquality,
independent_functionElimination,
independent_pairFormation,
lambdaFormation_alt,
productIsType,
universeIsType,
equalityIsType4,
because_Cache,
functionIsType,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[A,B:PType]. (p-and(A;B) \mmember{} PType)
Date html generated:
2019_10_31-AM-07_19_54
Last ObjectModification:
2018_10_15-PM-01_27_50
Theory : lattices
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