Nuprl Lemma : Girard-theorem
¬(Type ∈ Type)
Proof
Definitions occuring in Statement :
not: ¬A,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
WFO: WFO{i:l}(),
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
max-WO: max-WO{i:l}(),
order-type-less: order-type-less(),
spreadn: spread3,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
infix_ap: x f y,
so_apply: x[s],
all: ∀x:A. B[x],
WFTRO: WFTRO{i:l}(),
max-WFTO: max-WFTO{i:l}(),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
DCC: DCC(T;<),
false: False,
uimplies: b supposing a,
top: Top
Lemmas referenced :
DCC_wf,
exists_wf,
order-preserving_wf,
infix_ap_wf,
istype-universe,
all_wf,
DCC-order-type_wf,
order-type-less-maximal-ext,
ot-less-trans_wf,
trans_wf,
order-type-less_wf,
subtype_rel_self,
DCC-order-type-less-ext,
nat_wf,
WFO_wf,
istype-top,
subtype_rel_dep_function,
top_wf,
istype-void
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
productEquality,
sqequalHypSubstitution,
equalityTransitivity,
hypothesis,
equalitySymmetry,
functionEquality,
hypothesisEquality,
because_Cache,
introduction,
extract_by_obid,
isectElimination,
thin,
dependent_pairEquality_alt,
sqequalRule,
lambdaEquality_alt,
productElimination,
inhabitedIsType,
applyEquality,
functionIsType,
productIsType,
universeIsType,
rename,
dependent_functionElimination,
independent_pairEquality,
dependent_pairFormation_alt,
instantiate,
universeEquality,
functionExtensionality,
independent_functionElimination,
voidElimination,
cumulativity,
independent_isectElimination,
isect_memberEquality_alt,
equalityIsType4,
baseClosed
Latex:
\mneg{}(Type \mmember{} Type)
Date html generated:
2019_10_15-AM-11_10_59
Last ObjectModification:
2018_10_10-PM-02_05_09
Theory : general
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