Nuprl Lemma : partial-base
partial(Base) ⊆r Base
Proof
Definitions occuring in Statement :
partial: partial(T),
subtype_rel: A ⊆r B,
base: Base
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
partial: partial(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
base-partial: base-partial(T),
prop: ℙ,
per-partial: per-partial(T;x;y),
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
not: ¬A,
false: False
Lemmas referenced :
base_wf,
per-partial_wf,
base-partial_wf,
partial_wf,
subtype_base_sq,
subtype_rel_self,
has-value_wf_base,
is-exception_wf,
base-partial-not-exception
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
thin,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
rename,
Error :universeIsType,
isectElimination,
hypothesisEquality,
applyEquality,
setElimination,
Error :equalityIsType1,
dependent_functionElimination,
independent_functionElimination,
Error :productIsType,
Error :equalityIsType4,
because_Cache,
sqequalSqle,
divergentSqle,
independent_isectElimination,
instantiate,
cumulativity,
sqleReflexivity,
voidElimination
Latex:
partial(Base) \msubseteq{}r Base
Date html generated:
2019_06_20-PM-00_33_49
Last ObjectModification:
2018_10_27-AM-11_07_53
Theory : partial_1
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