Nuprl Lemma : fun_thru_2op_wf
∀[A,B:Type]. ∀[opa:A ⟶ A ⟶ A]. ∀[opb:B ⟶ B ⟶ B]. ∀[f:A ⟶ B]. (FunThru2op(A;B;opa;opb;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s]
Lemmas referenced :
uall_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[opa:A {}\mrightarrow{} A {}\mrightarrow{} A]. \mforall{}[opb:B {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[f:A {}\mrightarrow{} B]. (FunThru2op(A;B;opa;opb;f) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_02_49
Last ObjectModification:
2015_12_26-PM-11_25_13
Theory : gen_algebra_1
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