Nuprl Lemma : fun_thru_1op_wf

[A,B:Type]. ∀[opa:A ⟶ A]. ∀[opb:B ⟶ B]. ∀[f:A ⟶ B].  (fun_thru_1op(A;B;opa;opb;f) ∈ ℙ)


Proof




Definitions occuring in Statement :  fun_thru_1op: fun_thru_1op(A;B;opa;opb;f) uall: [x:A]. B[x] prop: member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  fun_thru_1op: fun_thru_1op(A;B;opa;opb;f) uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] 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].  \mforall{}[opb:B  {}\mrightarrow{}  B].  \mforall{}[f:A  {}\mrightarrow{}  B].    (fun\_thru\_1op(A;B;opa;opb;f)  \mmember{}  \mBbbP{})



Date html generated: 2016_05_15-PM-00_02_43
Last ObjectModification: 2015_12_26-PM-11_25_25

Theory : gen_algebra_1


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