Nuprl Lemma : retract_wf
∀[T:Type]. ∀[f:Base]. retract(T;f) ∈ ℙ supposing T ⊆r Base
Proof
Definitions occuring in Statement :
retract: retract(T;f),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
retract: retract(T;f),
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
all_wf,
and_wf,
has-value_wf_base,
equal-wf-base,
base_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
functionEquality,
lambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}[f:Base]. retract(T;f) \mmember{} \mBbbP{} supposing T \msubseteq{}r Base
Date html generated:
2016_05_14-PM-03_31_34
Last ObjectModification:
2016_01_14-PM-11_19_23
Theory : decidable!equality
Home
Index