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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