Nuprl Lemma : branch_wf2
∀[P:ℙ]. ∀[d:Dec(P)]. ∀[T:Type]. ∀[A:P ⟶ T]. ∀[B:⋂q:¬P. T]. (if p:P then A[p] else B fi ∈ T)
Proof
Definitions occuring in Statement :
branch: if p:P then A[p] else B fi ,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
not: ¬A,
member: t ∈ T,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
branch: if p:P then A[p] else B fi ,
decidable: Dec(P),
or: P ∨ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
not_wf,
decidable_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalHypSubstitution,
unionElimination,
thin,
sqequalRule,
isectEquality,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
because_Cache,
functionEquality,
universeEquality,
isect_memberFormation,
introduction,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
applyEquality
Latex:
\mforall{}[P:\mBbbP{}]. \mforall{}[d:Dec(P)]. \mforall{}[T:Type]. \mforall{}[A:P {}\mrightarrow{} T]. \mforall{}[B:\mcap{}q:\mneg{}P. T]. (if p:P then A[p] else B fi \mmember{} T)
Date html generated:
2016_05_15-PM-03_28_12
Last ObjectModification:
2015_12_27-PM-01_09_11
Theory : general
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