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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