Nuprl Lemma : zero-le-nat
∀[i:ℕ]. (0 ≤ i)
Proof
Definitions occuring in Statement :
nat: ℕ,
uall: ∀[x:A]. B[x],
le: A ≤ B,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
squash: ↓T,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
prop: ℙ
Lemmas referenced :
nat_wf,
less_than'_wf,
decidable__le,
le_wf,
sq_stable_from_decidable
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
natural_numberEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
independent_pairEquality,
lambdaEquality,
voidElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[i:\mBbbN{}]. (0 \mleq{} i)
Date html generated:
2016_05_13-PM-03_32_06
Last ObjectModification:
2016_01_14-PM-06_40_54
Theory : arithmetic
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