Nuprl Lemma : nat-weak-overt
wOvert(ℕ)
Proof
Definitions occuring in Statement :
weak-overt: wOvert(X),
nat: ℕ
Definitions unfolded in proof :
weak-overt: wOvert(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
prop: ℙ,
Open: Open(X),
so_lambda: λ2x.t[x],
so_apply: x[s],
in-open: x ∈ A,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
rev_implies: P ⇐ Q
Lemmas referenced :
sp-lub_wf,
nat_wf,
Sierpinski_wf,
not_wf,
exists_wf,
equal-wf-T-base,
Open_wf,
sp-lub-is-top,
iff_wf,
all_wf,
in-open_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
universeEquality,
dependent_pairFormation,
lambdaEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
applyEquality,
functionExtensionality,
hypothesisEquality,
productEquality,
hypothesis,
cumulativity,
independent_pairEquality,
functionEquality,
lambdaFormation,
productElimination,
dependent_functionElimination,
voidElimination,
baseClosed,
axiomEquality,
independent_pairFormation,
because_Cache,
addLevel,
impliesFunctionality,
independent_functionElimination
Latex:
wOvert(\mBbbN{})
Date html generated:
2019_10_31-AM-07_19_20
Last ObjectModification:
2017_07_28-AM-09_12_27
Theory : synthetic!topology
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