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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