Nuprl Lemma : imagetype_wf
∀[A:Type]. ∀[f:Base]. (imagetype(A;f) ∈ Type)
Proof
Definitions occuring in Statement :
imagetype: imagetype(A;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
imagetype: imagetype(A;f),
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s1;s2],
prop: ℙ,
guard: {T},
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y])
Lemmas referenced :
image-per-transitive,
pertype_wf,
image-per_wf,
base_wf,
image-per-symmetric
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
cumulativity,
independent_isectElimination,
lambdaFormation,
applyEquality,
because_Cache,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[A:Type]. \mforall{}[f:Base]. (imagetype(A;f) \mmember{} Type)
Date html generated:
2019_06_20-PM-02_02_42
Last ObjectModification:
2018_09_05-PM-09_17_27
Theory : relations2
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