Nuprl Lemma : reciprocal-qle
∀e:ℚ. ∃m:ℕ+. ((1/m) ≤ e) supposing 0 < e
Proof
Definitions occuring in Statement :
qle: r ≤ s,
qless: r < s,
qdiv: (r/s),
rationals: ℚ,
nat_plus: ℕ+,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
experimental: experimental{impliesFunctionality}(possibleextract),
reciprocal-qle-proof,
q-elim,
decidable__equal_int,
qle_reflexivity,
rem_bounds_1,
qmul_preserves_qle,
any: any x,
decidable__int_equal,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
reciprocal-qle-proof,
lifting-strict-spread,
istype-void,
strict4-spread,
lifting-strict-int_eq,
strict4-decide,
q-elim,
decidable__equal_int,
qle_reflexivity,
rem_bounds_1,
qmul_preserves_qle,
decidable__int_equal
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
isect_memberEquality_alt,
voidElimination,
independent_isectElimination
Latex:
\mforall{}e:\mBbbQ{}. \mexists{}m:\mBbbN{}\msupplus{}. ((1/m) \mleq{} e) supposing 0 < e
Date html generated:
2019_10_16-PM-00_32_20
Last ObjectModification:
2019_06_26-PM-04_16_03
Theory : rationals
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