Nuprl Lemma : continuous'-monotone-identity
continuous'-monotone{i:l}(T.T)
Proof
Definitions occuring in Statement :
continuous'-monotone: continuous'-monotone{i:l}(T.F[T])
Definitions unfolded in proof :
continuous'-monotone: continuous'-monotone{i:l}(T.F[T]),
and: P ∧ Q,
cand: A c∧ B,
type-monotone: Monotone(T.F[T]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
type-continuous': semi-continuous(λT.F[T]),
so_lambda: λ2x.t[x],
type-incr-chain: type-incr-chain{i:l}(),
so_apply: x[s]
Lemmas referenced :
subtype_rel_wf,
subtype_rel_self,
tunion_wf,
nat_wf,
type-incr-chain_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
isect_memberFormation,
introduction,
hypothesis,
sqequalRule,
axiomEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
independent_pairFormation,
lambdaEquality,
applyEquality,
setElimination,
rename
Latex:
continuous'-monotone\{i:l\}(T.T)
Date html generated:
2016_05_15-PM-06_53_53
Last ObjectModification:
2015_12_27-AM-11_41_37
Theory : general
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