Nuprl Lemma : nat-overt
Overt(ℕ)
Proof
Definitions occuring in Statement :
overt: Overt(X),
nat: ℕ
Definitions unfolded in proof :
overt: Overt(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
Open: Open(X),
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
sp-le: x ≤ y,
guard: {T}
Lemmas referenced :
sp-lub_wf,
nat_wf,
Sierpinski_wf,
Open_wf,
all_wf,
sp-le_wf,
equal-wf-T-base,
iff_wf,
sp-lub-property
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
universeEquality,
dependent_pairFormation,
lambdaEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
applyEquality,
hypothesisEquality,
independent_pairEquality,
hypothesis,
cumulativity,
functionEquality,
productEquality,
lambdaFormation,
independent_pairFormation,
productElimination,
dependent_functionElimination,
axiomEquality,
baseClosed,
because_Cache,
functionExtensionality,
independent_functionElimination
Latex:
Overt(\mBbbN{})
Date html generated:
2019_10_31-AM-07_19_09
Last ObjectModification:
2017_07_28-AM-09_12_24
Theory : synthetic!topology
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