Nuprl Lemma : itermConstant_wf

[const:ℤ]. ("const" ∈ int_term())


Proof




Definitions occuring in Statement :  itermConstant: "const" int_term: int_term() uall: [x:A]. B[x] member: t ∈ T int:
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T int_term: int_term() itermConstant: "const" eq_atom: =a y ifthenelse: if then else fi  btrue: tt subtype_rel: A ⊆B ext-eq: A ≡ B and: P ∧ Q int_termco_size: int_termco_size(p) int_term_size: int_term_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_termco-ext ifthenelse_wf eq_atom_wf int_termco_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 int_termco_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 thin instantiate sqequalHypSubstitution isectElimination universeEquality intEquality productEquality voidEquality applyEquality productElimination natural_numberEquality independent_pairFormation lambdaFormation divergentSqle sqleReflexivity because_Cache lambdaEquality independent_isectElimination equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination

Latex:
\mforall{}[const:\mBbbZ{}].  ("const"  \mmember{}  int\_term())



Date html generated: 2017_04_14-AM-08_56_29
Last ObjectModification: 2017_02_27-PM-03_39_58

Theory : omega


Home Index