Nuprl Lemma : sqequal-list_ind

        F[rec-case(as) of
          [] => b1
          h::t =>
           r.H[h;t;r]] G[rec-case(as) of
                           [] => b2
                           h::t =>
        supposing F[b1] G[b2] 
      supposing (∀x,y,r1,r2:Base.  ((F[r1] ≤ G[r2])  (F[H[x;y;r1]] ≤ G[J[x;y;r2]])))
      ∧ (∀x,y,r1,r2:Base.  ((G[r1] ≤ F[r2])  (G[J[x;y;r1]] ≤ F[H[x;y;r2]]))) 
    supposing strict1(λx.G[x]) 
  supposing strict1(λx.F[x])


Definitions occuring in Statement :  list_ind: list_ind strict1: strict1(F) uimplies: supposing a uall: [x:A]. B[x] so_apply: x[s1;s2;s3] so_apply: x[s] all: x:A. B[x] implies:  Q and: P ∧ Q lambda: λx.A[x] base: Base sqle: s ≤ t sqequal: t
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a all: x:A. B[x] and: P ∧ Q cand: c∧ B prop: so_lambda: λ2x.t[x] implies:  Q so_apply: x[s] so_apply: x[s1;s2;s3]
Lemmas referenced :  strict1_wf sqle_wf_base all_wf base_wf sqle-list_ind
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaFormation sqequalSqle sqequalHypSubstitution productElimination thin lemma_by_obid isectElimination hypothesisEquality independent_isectElimination hypothesis dependent_functionElimination sqequalRule sqleReflexivity sqequalAxiom sqequalIntensionalEquality baseApply closedConclusion baseClosed lambdaEquality isect_memberEquality because_Cache equalityTransitivity equalitySymmetry productEquality functionEquality

                F[rec-case(as)  of
                    []  =>  b1
                    h::t  =>
                      r.H[h;t;r]]  \msim{}  G[rec-case(as)  of
                                                      []  =>  b2
                                                      h::t  =>
                supposing  F[b1]  \msim{}  G[b2] 
            supposing  (\mforall{}x,y,r1,r2:Base.    ((F[r1]  \mleq{}  G[r2])  {}\mRightarrow{}  (F[H[x;y;r1]]  \mleq{}  G[J[x;y;r2]])))
            \mwedge{}  (\mforall{}x,y,r1,r2:Base.    ((G[r1]  \mleq{}  F[r2])  {}\mRightarrow{}  (G[J[x;y;r1]]  \mleq{}  F[H[x;y;r2]]))) 
        supposing  strict1(\mlambda{}x.G[x]) 
    supposing  strict1(\mlambda{}x.F[x])

Date html generated: 2016_05_14-AM-06_29_05
Last ObjectModification: 2016_01_14-PM-08_25_48

Theory : list_0

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