Nuprl Lemma : spread_to_pi12
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[p:x:A × B[x]]. ∀[C:Type]. ∀[b:x:A ⟶ B[x] ⟶ C].
(let x,y = p in b[x;y] = b[fst(p);snd(p)] ∈ C)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
function: x:A ⟶ B[x],
spread: spread def,
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi1: fst(t),
pi2: snd(t),
so_apply: x[s1;s2],
so_apply: x[s]
Lemmas referenced :
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
productElimination,
thin,
sqequalRule,
applyEquality,
hypothesisEquality,
hypothesis,
Error :functionIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
Error :universeIsType,
Error :isect_memberEquality_alt,
axiomEquality,
Error :inhabitedIsType,
because_Cache,
Error :productIsType,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[p:x:A \mtimes{} B[x]]. \mforall{}[C:Type]. \mforall{}[b:x:A {}\mrightarrow{} B[x] {}\mrightarrow{} C].
(let x,y = p in b[x;y] = b[fst(p);snd(p)])
Date html generated:
2019_06_20-AM-11_18_01
Last ObjectModification:
2018_10_06-AM-09_00_16
Theory : core_2
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