Nuprl Lemma : intformless_wf

[left,right:int_term()].  ((left "<right) ∈ int_formula())


Proof




Definitions occuring in Statement :  intformless: (left "<right) int_formula: int_formula() int_term: int_term() uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T int_formula: int_formula() intformless: (left "<right) eq_atom: =a y ifthenelse: if then else fi  btrue: tt subtype_rel: A ⊆B ext-eq: A ≡ B and: P ∧ Q int_formulaco_size: int_formulaco_size(p) int_formula_size: int_formula_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 :  int_formulaco-ext ifthenelse_wf eq_atom_wf int_term_wf int_formulaco_wf istype-void le_wf has-value_wf_base set_subtype_base istype-int int_subtype_base is-exception_wf has-value_wf-partial nat_wf set-value-type int-value-type int_formulaco_size_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  cut Error :dependent_set_memberEquality_alt,  introduction extract_by_obid hypothesis sqequalRule Error :dependent_pairEquality_alt,  tokenEquality hypothesisEquality Error :inhabitedIsType,  Error :universeIsType,  thin instantiate sqequalHypSubstitution isectElimination universeEquality productEquality voidEquality applyEquality productElimination natural_numberEquality independent_pairFormation Error :lambdaFormation_alt,  divergentSqle sqleReflexivity intEquality Error :lambdaEquality_alt,  independent_isectElimination because_Cache Error :equalityIsType1,  equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination

Latex:
\mforall{}[left,right:int\_term()].    ((left  "<"  right)  \mmember{}  int\_formula())



Date html generated: 2019_06_20-PM-00_46_07
Last ObjectModification: 2018_10_03-AM-00_45_41

Theory : omega


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