Nuprl Lemma : inductively-defined_wf
∀[R:Set{i:l} ⟶ Set{i:l} ⟶ ℙ']. ∀[s:Set{i:l}]. (inductively-defined{i:l}(x,a.R[x;a];s) ∈ ℙ')
Proof
Definitions occuring in Statement :
inductively-defined: inductively-defined{i:l}(x,a.R[x; a];s),
Set: Set{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
so_apply: x[s],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
and: P ∧ Q,
prop: ℙ,
inductively-defined: inductively-defined{i:l}(x,a.R[x; a];s),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
setsubset_wf,
all_wf,
Set_wf,
relclosed-set_wf
Rules used in proof :
universeEquality,
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
cumulativity,
functionEquality,
instantiate,
hypothesis,
hypothesisEquality,
applyEquality,
lambdaEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[R:Set\{i:l\} {}\mrightarrow{} Set\{i:l\} {}\mrightarrow{} \mBbbP{}']. \mforall{}[s:Set\{i:l\}]. (inductively-defined\{i:l\}(x,a.R[x;a];s) \mmember{} \mBbbP{}')
Date html generated:
2018_05_29-PM-01_54_22
Last ObjectModification:
2018_05_25-PM-05_21_51
Theory : constructive!set!theory
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