Nuprl Lemma : compact-finite
∀n:ℕ. compact-type(ℕn)
Proof
Definitions occuring in Statement :
compact-type: compact-type(T),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
compact-type: compact-type(T),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
guard: {T},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
bfalse: ff,
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
true: True,
rev_implies: P ⇐ Q,
false: False,
not: ¬A,
exists: ∃x:A. B[x]
Lemmas referenced :
int_seg_wf,
bool_wf,
nat_wf,
decidable__exists_int_seg,
equal-wf-T-base,
decidable__equal_bool,
bfalse_wf,
all_wf,
exists_wf,
iff_imp_equal_bool,
btrue_wf,
false_wf,
true_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
functionEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
instantiate,
dependent_functionElimination,
lambdaEquality,
applyEquality,
functionExtensionality,
baseClosed,
because_Cache,
independent_functionElimination,
unionElimination,
inlFormation,
inrFormation,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
independent_pairFormation,
dependent_pairFormation
Latex:
\mforall{}n:\mBbbN{}. compact-type(\mBbbN{}n)
Date html generated:
2017_10_01-AM-08_29_02
Last ObjectModification:
2017_07_26-PM-04_23_47
Theory : basic
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