Nuprl Lemma : mFOatomic_wf

[name:Atom]. ∀[vars:ℤ List].  (name(vars) ∈ mFOL())


Proof




Definitions occuring in Statement :  mFOatomic: name(vars) mFOL: mFOL() list: List uall: [x:A]. B[x] member: t ∈ T int: atom: Atom
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T mFOL: mFOL() mFOatomic: name(vars) eq_atom: =a y ifthenelse: if then else fi  btrue: tt subtype_rel: A ⊆B ext-eq: A ≡ B and: P ∧ Q mFOLco_size: mFOLco_size(p) mFOL_size: mFOL_size(p) has-value: (a)↓ nat: le: A ≤ B less_than': less_than'(a;b) false: False not: ¬A implies:  Q prop: all: x:A. B[x] so_lambda: λ2x.t[x] so_apply: x[s] uimplies: supposing a
Lemmas referenced :  mFOLco-ext list_wf ifthenelse_wf eq_atom_wf mFOLco_wf bool_wf false_wf le_wf nat_wf has-value_wf_base set_subtype_base int_subtype_base is-exception_wf equal_wf has-value_wf-partial set-value-type int-value-type mFOLco_size_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut dependent_set_memberEquality introduction extract_by_obid hypothesis sqequalRule dependent_pairEquality tokenEquality hypothesisEquality sqequalHypSubstitution isectElimination thin intEquality instantiate universeEquality productEquality atomEquality voidEquality applyEquality productElimination natural_numberEquality independent_pairFormation lambdaFormation divergentSqle sqleReflexivity lambdaEquality independent_isectElimination because_Cache equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination

Latex:
\mforall{}[name:Atom].  \mforall{}[vars:\mBbbZ{}  List].    (name(vars)  \mmember{}  mFOL())



Date html generated: 2018_05_21-PM-10_20_53
Last ObjectModification: 2017_07_26-PM-06_37_39

Theory : minimal-first-order-logic


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