Nuprl Lemma : nat_plus_subtype_nat
ℕ+ ⊆r ℕ
Proof
Definitions occuring in Statement :
nat_plus: ℕ+,
nat: ℕ,
subtype_rel: A ⊆r B
Definitions unfolded in proof :
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
subtype_rel_sets,
less_than_wf,
le_wf,
le_weakening2
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
because_Cache,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
setElimination,
rename,
setEquality,
lambdaFormation,
dependent_functionElimination
Latex:
\mBbbN{}\msupplus{} \msubseteq{}r \mBbbN{}
Date html generated:
2016_05_13-PM-03_32_14
Last ObjectModification:
2015_12_26-AM-09_45_32
Theory : arithmetic
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