Nuprl Lemma : image-per_wf
∀[A:Type]. ∀[f:Base]. (image-per(A;f) ∈ Base ⟶ Base ⟶ ℙ)
Proof
Definitions occuring in Statement :
image-per: image-per(A;f),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
image-per: image-per(A;f),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
usquash_wf,
transitive-closure_wf,
base_wf,
exists_wf,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesis,
productEquality,
hypothesisEquality,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[f:Base]. (image-per(A;f) \mmember{} Base {}\mrightarrow{} Base {}\mrightarrow{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_02_32
Last ObjectModification:
2018_09_05-PM-08_26_40
Theory : relations2
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