Nuprl Lemma : branch_wf
∀[P:ℙ]. ∀[d:Dec(P)]. ∀[T:Type]. ∀[A:P ⟶ T]. ∀[B: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],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
branch: if p:P then A[p] else B fi ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s]
Lemmas referenced :
not_wf,
equal_wf,
decidable_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
unionEquality,
cumulativity,
extract_by_obid,
isectElimination,
lambdaFormation,
unionElimination,
applyEquality,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[P:\mBbbP{}]. \mforall{}[d:Dec(P)]. \mforall{}[T:Type]. \mforall{}[A:P {}\mrightarrow{} T]. \mforall{}[B:T]. (if p:P then A[p] else B fi \mmember{} T)
Date html generated:
2019_10_15-AM-11_07_10
Last ObjectModification:
2018_08_21-PM-01_58_56
Theory : general
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