Nuprl Lemma : pimp_wf

[left,right:formula()].  (pimp(left;right) ∈ formula())


Proof




Definitions occuring in Statement :  pimp: pimp(left;right) formula: formula() uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T formula: formula() pimp: pimp(left;right) eq_atom: =a y ifthenelse: if then else fi  bfalse: ff btrue: tt subtype_rel: A ⊆B ext-eq: A ≡ B and: P ∧ Q formulaco_size: formulaco_size(p) formula_size: formula_size(p) nat: le: A ≤ B less_than': less_than'(a;b) false: False not: ¬A implies:  Q prop: all: x:A. B[x] uimplies: supposing a so_lambda: λ2x.t[x] so_apply: x[s]
Lemmas referenced :  formulaco-ext formulaco_wf ifthenelse_wf eq_atom_wf add_nat_wf false_wf le_wf formula_size_wf nat_wf value-type-has-value set-value-type int-value-type equal_wf has-value_wf-partial formulaco_size_wf formula_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut dependent_set_memberEquality introduction extract_by_obid hypothesis sqequalRule dependent_pairEquality tokenEquality sqequalHypSubstitution setElimination thin rename hypothesisEquality instantiate isectElimination universeEquality atomEquality productEquality voidEquality applyEquality productElimination natural_numberEquality independent_pairFormation lambdaFormation independent_isectElimination intEquality lambdaEquality equalityTransitivity equalitySymmetry dependent_functionElimination independent_functionElimination

Latex:
\mforall{}[left,right:formula()].    (pimp(left;right)  \mmember{}  formula())



Date html generated: 2018_05_21-PM-08_48_56
Last ObjectModification: 2017_07_26-PM-06_11_58

Theory : general


Home Index