Nuprl Lemma : AF-spread-law_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (AF-spread-law(x,y.R[x;y]) ∈ n:ℕ ⟶ (ℕn ⟶ (T?)) ⟶ (T?) ⟶ ℙ)
Proof
Definitions occuring in Statement :
AF-spread-law: AF-spread-law(x,y.R[x; y]),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
AF-spread-law: AF-spread-law(x,y.R[x; y]),
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s1;s2],
uimplies: b supposing a,
outl: outl(x),
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
assert_wf,
isl_wf,
unit_wf2,
all_wf,
int_seg_wf,
not_wf,
outl_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
functionEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
natural_numberEquality,
setElimination,
rename,
productEquality,
because_Cache,
applyEquality,
independent_isectElimination,
unionElimination,
voidElimination,
unionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (AF-spread-law(x,y.R[x;y]) \mmember{} n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} (T?)) {}\mrightarrow{} (T?) {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_50_56
Last ObjectModification:
2015_12_26-AM-10_17_25
Theory : bar-induction
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