Nuprl Lemma : extend_permf_over_id
∀n:ℕ. (extend_permf(Id;n) = Id ∈ (ℕn + 1 ⟶ ℕn + 1))
Proof
Definitions occuring in Statement :
extend_permf: extend_permf(pf;n)
,
identity: Id
,
int_seg: {i..j-}
,
nat: ℕ
,
all: ∀x:A. B[x]
,
function: x:A ⟶ B[x]
,
add: n + m
,
natural_number: $n
,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x]
,
member: t ∈ T
,
identity: Id
,
extend_permf: extend_permf(pf;n)
,
uall: ∀[x:A]. B[x]
,
int_seg: {i..j-}
,
nat: ℕ
,
implies: P
⇒ Q
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
uimplies: b supposing a
,
ifthenelse: if b then t else f fi
,
bfalse: ff
,
exists: ∃x:A. B[x]
,
subtype_rel: A ⊆r B
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
,
or: P ∨ Q
,
sq_type: SQType(T)
,
guard: {T}
,
bnot: ¬bb
,
assert: ↑b
,
false: False
Lemmas referenced :
nat_wf,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
lelt_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
lambdaEquality_alt,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
inhabitedIsType,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
independent_isectElimination,
dependent_pairFormation_alt,
equalityTransitivity,
equalitySymmetry,
equalityIsType2,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
intEquality,
natural_numberEquality,
addEquality,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
equalityIsType1
Latex:
\mforall{}n:\mBbbN{}. (extend\_permf(Id;n) = Id)
Date html generated:
2019_10_16-PM-00_59_51
Last ObjectModification:
2018_10_08-AM-09_20_22
Theory : perms_1
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