Nuprl Lemma : p-disjoint_wf
∀[A,B:Type]. ∀[f,g:A ⟶ (B + Top)]. (p-disjoint(A;f;g) ∈ ℙ)
Proof
Definitions occuring in Statement :
p-disjoint: p-disjoint(A;f;g),
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
p-disjoint: p-disjoint(A;f;g),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
all_wf,
not_wf,
assert_wf,
can-apply_wf,
subtype_rel_dep_function,
top_wf,
subtype_rel_union
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
productEquality,
because_Cache,
applyEquality,
unionEquality,
hypothesis,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f,g:A {}\mrightarrow{} (B + Top)]. (p-disjoint(A;f;g) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-03_46_06
Last ObjectModification:
2015_12_27-PM-01_20_29
Theory : general
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