Nuprl Lemma : type-mismatch_wf
∀[T,T1,T2,T3:Type]. ∀[f:T]. ∀[A:T1]. ∀[x:T2]. ∀[B:T3]. (type-mismatch(f; A; x; B) ∈ Unit)
Proof
Definitions occuring in Statement :
type-mismatch: type-mismatch(f; A; x; B),
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
type-mismatch: type-mismatch(f; A; x; B)
Lemmas referenced :
it_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
universeEquality
Latex:
\mforall{}[T,T1,T2,T3:Type]. \mforall{}[f:T]. \mforall{}[A:T1]. \mforall{}[x:T2]. \mforall{}[B:T3]. (type-mismatch(f; A; x; B) \mmember{} Unit)
Date html generated:
2016_05_15-PM-03_24_36
Last ObjectModification:
2015_12_27-PM-01_06_06
Theory : general
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