Nuprl Lemma : sq_stable__fun_thru_1op

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


Proof




Definitions occuring in Statement :  fun_thru_1op: fun_thru_1op(A;B;opa;opb;f) sq_stable: SqStable(P) uall: [x:A]. B[x] 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] implies:  Q sq_stable: SqStable(P) prop:
Lemmas referenced :  sq_stable__uall equal_wf sq_stable__equal squash_wf uall_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis independent_functionElimination dependent_functionElimination axiomEquality because_Cache isect_memberEquality functionEquality universeEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[opa:A  {}\mrightarrow{}  A].  \mforall{}[opb:B  {}\mrightarrow{}  B].  \mforall{}[f:A  {}\mrightarrow{}  B].    SqStable(fun\_thru\_1op(A;B;opa;opb;f))



Date html generated: 2016_05_15-PM-00_02_45
Last ObjectModification: 2015_12_26-PM-11_25_23

Theory : gen_algebra_1


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