Nuprl Lemma : polymorphic-id-unique-sq
∀f:⋂T:Type. (T ⟶ T). (f ~ λx.x)
Proof
Definitions occuring in Statement :
all: ∀x:A. B[x],
lambda: λx.A[x],
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T},
or: P ∨ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
it: ⋅,
top: Top,
unit: Unit,
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
squash: ↓T
Lemmas referenced :
value-type-has-value,
int-value-type,
istype-int,
istype-universe,
istype-base,
base_wf,
equal-wf-base,
subtype_base_sq,
set_subtype_base,
subtype_rel_self,
has-value_wf_base,
is-exception_wf,
unit_wf2,
it_wf,
unit_subtype_base,
equal-unit,
bottom-sqle,
istype-void,
equal-value-type,
bottom_diverge,
istype-sqequal
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
callbyvalueApplyCases,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
applyEquality,
hypothesisEquality,
natural_numberEquality,
Error :functionIsType,
because_Cache,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
Error :lambdaEquality_alt,
Error :isectIsType,
instantiate,
universeEquality,
Error :universeIsType,
sqequalRule,
unionElimination,
Error :equalityIstype,
sqequalBase,
setEquality,
Error :inhabitedIsType,
Error :dependent_set_memberEquality_alt,
setElimination,
rename,
cumulativity,
independent_functionElimination,
baseClosed,
axiomSqleEquality,
divergentSqle,
sqleReflexivity,
sqequalSqle,
Error :isect_memberEquality_alt,
voidElimination,
functionEquality,
isectEquality,
pointwiseFunctionality,
lambdaFormation,
axiomSqEquality,
sqequalExtensionalEquality,
independent_pairFormation,
imageMemberEquality
Latex:
\mforall{}f:\mcap{}T:Type. (T {}\mrightarrow{} T). (f \msim{} \mlambda{}x.x)
Date html generated:
2019_06_20-PM-02_44_07
Last ObjectModification:
2019_01_28-PM-01_36_44
Theory : num_thy_1
Home
Index