Nuprl Lemma : is-qrep_wf
∀p:ℤ × ℕ+. (is-qrep(p) ∈ 𝔹)
Proof
Definitions occuring in Statement :
is-qrep: is-qrep(p),
nat_plus: ℕ+,
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
is-qrep: is-qrep(p),
has-value: (a)↓,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
nat_plus: ℕ+
Lemmas referenced :
value-type-has-value,
int-value-type,
better-gcd_wf,
bor_wf,
eq_int_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
productElimination,
thin,
callbyvalueReduce,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
setElimination,
rename,
natural_numberEquality,
minusEquality,
productEquality
Latex:
\mforall{}p:\mBbbZ{} \mtimes{} \mBbbN{}\msupplus{}. (is-qrep(p) \mmember{} \mBbbB{})
Date html generated:
2016_05_15-PM-10_40_04
Last ObjectModification:
2015_12_27-PM-07_58_37
Theory : rationals
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