Nuprl Lemma : update_wf
∀[A,B:Type]. ∀[eq:A ⟶ A ⟶ 𝔹]. ∀[f:A ⟶ B]. ∀[x:A]. ∀[v:B]. (f[x:=v] ∈ A ⟶ B)
Proof
Definitions occuring in Statement :
update: f[x:=v],
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
update: f[x:=v],
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
ifthenelse_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[eq:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[x:A]. \mforall{}[v:B]. (f[x:=v] \mmember{} A {}\mrightarrow{} B)
Date html generated:
2016_05_15-PM-03_49_13
Last ObjectModification:
2015_12_27-PM-01_22_00
Theory : general
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