Nuprl Lemma : bag-order_wf
∀T:Type. (bag-order(T) ∈ Type)
Proof
Definitions occuring in Statement :
bag-order: bag-order(T),
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
bag-order: bag-order(T),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
so_lambda: λ2x.t[x],
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
gt: i > j,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
le_wf,
linorder_wf,
gt_wf,
less_than_wf,
equal_wf,
equal-wf-T-base,
iff_wf,
all_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
setEquality,
functionEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
intEquality,
productEquality,
lambdaEquality,
applyEquality,
baseClosed,
natural_numberEquality,
universeEquality
Latex:
\mforall{}T:Type. (bag-order(T) \mmember{} Type)
Date html generated:
2016_05_15-PM-03_11_23
Last ObjectModification:
2016_01_16-AM-08_37_23
Theory : bags
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