Nuprl Lemma : compact-dCCC
∀K:Type. (K ⇒ compact-type(K) ⇒ dCCC(K))
Proof
Definitions occuring in Statement :
compact-type: compact-type(T),
contra-dcc: dCCC(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
contra-dcc: dCCC(T),
compact-type: compact-type(T),
member: t ∈ T,
or: P ∨ Q,
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
not: ¬A,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
pi1: fst(t)
Lemmas referenced :
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_of_ff,
istype-assert,
istype-void,
assert_of_tt,
istype-nat,
compact-type_wf,
istype-universe,
nat_wf,
pi1_wf,
not_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
lambdaEquality_alt,
applyEquality,
hypothesisEquality,
inhabitedIsType,
sqequalRule,
unionElimination,
inlFormation_alt,
productElimination,
dependent_pairFormation_alt,
instantiate,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesis,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
functionIsType,
because_Cache,
inrFormation_alt,
productIsType,
rename,
universeIsType,
universeEquality,
functionExtensionality,
dependent_pairEquality_alt,
equalityIstype,
voidElimination
Latex:
\mforall{}K:Type. (K {}\mRightarrow{} compact-type(K) {}\mRightarrow{} dCCC(K))
Date html generated:
2019_10_15-AM-10_47_09
Last ObjectModification:
2019_06_20-AM-11_02_07
Theory : basic
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