Nuprl Lemma : int-prod-single
∀[f:Top]. (Π(f[x] | x < 1) ~ 1 * f[0])
Proof
Definitions occuring in Statement :
int-prod: Π(f[x] | x < k),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
multiply: n * m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
bfalse: ff,
ifthenelse: if b then t else f fi ,
subtract: n - m,
eq_int: (i =z j),
so_apply: x[s],
top: Top,
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf,
int_prod0_lemma,
le_wf,
false_wf,
int-prod-unroll-hi
Rules used in proof :
sqequalAxiom,
dependent_functionElimination,
voidEquality,
voidElimination,
isect_memberEquality,
hypothesisEquality,
hypothesis,
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[f:Top]. (\mPi{}(f[x] | x < 1) \msim{} 1 * f[0])
Date html generated:
2018_05_21-PM-00_28_55
Last ObjectModification:
2017_12_10-PM-11_39_56
Theory : int_2
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