Nuprl Lemma : bounded-type-cantor
Bounded(ℕ ⟶ 𝔹)
Proof
Definitions occuring in Statement :
bounded-type: Bounded(T),
nat: ℕ,
bool: 𝔹,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
uimplies: b supposing a,
true: True,
prop: ℙ,
uall: ∀[x:A]. B[x],
squash: ↓T,
sq_exists: ∃x:A [B[x]],
exists: ∃x:A. B[x],
nat: ℕ,
subtype_rel: A ⊆r B,
member: t ∈ T,
all: ∀x:A. B[x],
bounded-type: Bounded(T)
Lemmas referenced :
istype-nat,
istype-le,
iff_weakening_equal,
subtype_rel_self,
absval_pos,
istype-int,
true_wf,
squash_wf,
le_wf,
bool_wf,
nat_wf,
cantor-to-int-bounded
Rules used in proof :
functionIsType,
independent_functionElimination,
independent_isectElimination,
universeEquality,
instantiate,
baseClosed,
imageMemberEquality,
natural_numberEquality,
inhabitedIsType,
universeIsType,
equalitySymmetry,
equalityTransitivity,
isectElimination,
imageElimination,
dependent_set_memberEquality_alt,
productElimination,
functionEquality,
closedConclusion,
sqequalRule,
because_Cache,
rename,
setElimination,
lambdaEquality_alt,
hypothesis,
hypothesisEquality,
applyEquality,
functionExtensionality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
Bounded(\mBbbN{} {}\mrightarrow{} \mBbbB{})
Date html generated:
2019_10_15-AM-10_26_23
Last ObjectModification:
2019_10_07-PM-04_52_56
Theory : continuity
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