### Nuprl Lemma : has-valueall-pair

`∀[a,b:Base].  uiff(has-valueall(<a, b>);has-valueall(a) ∧ has-valueall(b))`

Proof

Definitions occuring in Statement :  has-valueall: `has-valueall(a)` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` and: `P ∧ Q` pair: `<a, b>` base: `Base`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` has-valueall: `has-valueall(a)` top: `Top` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` has-value: `(a)↓` prop: `ℙ` evalall: `evalall(t)`
Lemmas referenced :  base_wf has-valueall_wf_base and_wf is-exception_wf has-value_wf_base evalall-pair
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin isect_memberEquality voidElimination voidEquality hypothesis independent_pairFormation callbyvalueCallbyvalue callbyvalueReduce productElimination independent_pairEquality axiomSqleEquality baseApply closedConclusion baseClosed hypothesisEquality callbyvalueIspair divergentSqle sqleReflexivity equalityTransitivity equalitySymmetry because_Cache

Latex:
\mforall{}[a,b:Base].    uiff(has-valueall(<a,  b>);has-valueall(a)  \mwedge{}  has-valueall(b))

Date html generated: 2016_05_13-PM-03_25_28
Last ObjectModification: 2016_01_14-PM-06_45_22

Theory : call!by!value_1

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