Nuprl Lemma : image-per-transitive
∀[A:Type]. ∀[f:Base]. Trans(Base;x,y.image-per(A;f) x y)
Proof
Definitions occuring in Statement :
image-per: image-per(A;f),
trans: Trans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
apply: f a,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
image-per: image-per(A;f),
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
trans: Trans(T;x,y.E[x; y]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
usquash: usquash(T),
top: Top,
subtype_rel: A ⊆r B,
utrans: UniformlyTrans(T;x,y.E[x; y]),
exists: ∃x:A. B[x],
infix_ap: x f y
Lemmas referenced :
transitive-closure-transitive,
exists_wf,
base_wf,
equal-wf-base,
usquash_wf,
transitive-closure_wf,
implies-usquash,
istype-void
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
sqequalRule,
Error :lambdaEquality_alt,
hypothesis,
productEquality,
sqequalIntensionalEquality,
hypothesisEquality,
baseApply,
closedConclusion,
baseClosed,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality,
Error :lambdaFormation_alt,
applyEquality,
Error :pertypeElimination2,
independent_functionElimination,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}[A:Type]. \mforall{}[f:Base]. Trans(Base;x,y.image-per(A;f) x y)
Date html generated:
2019_06_20-PM-02_02_35
Last ObjectModification:
2018_10_07-AM-00_50_51
Theory : relations2
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