Nuprl Lemma : pimp?_wf

[v:formula()]. (pimp?(v) ∈ 𝔹)


Proof




Definitions occuring in Statement :  pimp?: pimp?(v) formula: formula() bool: 𝔹 uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T ext-eq: A ≡ B and: P ∧ Q subtype_rel: A ⊆B all: x:A. B[x] implies:  Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) uimplies: supposing a sq_type: SQType(T) guard: {T} eq_atom: =a y ifthenelse: if then else fi  pvar: pvar(name) pimp?: pimp?(v) pi1: fst(t) bfalse: ff exists: x:A. B[x] prop: or: P ∨ Q bnot: ¬bb assert: b false: False pnot: pnot(sub) pand: pand(left;right) por: por(left;right) pimp: pimp(left;right)
Lemmas referenced :  formula-ext eq_atom_wf bool_wf eqtt_to_assert assert_of_eq_atom subtype_base_sq atom_subtype_base bfalse_wf eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_atom btrue_wf formula_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut introduction extract_by_obid promote_hyp sqequalHypSubstitution productElimination thin hypothesis_subsumption hypothesis hypothesisEquality applyEquality sqequalRule isectElimination tokenEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry independent_isectElimination instantiate cumulativity atomEquality dependent_functionElimination independent_functionElimination because_Cache dependent_pairFormation voidElimination

Latex:
\mforall{}[v:formula()].  (pimp?(v)  \mmember{}  \mBbbB{})



Date html generated: 2018_05_21-PM-08_51_27
Last ObjectModification: 2017_07_26-PM-06_14_36

Theory : general


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