Nuprl Lemma : ctt-kind-1

[t:CttTerm]
  ∀X:?CubicalContext. [[X;t]] ⊆Provisional''''(cttType(context-set(X))) supposing context-ok(X) 
  supposing ctt-kind(t) 1 ∈ ℤ


Proof




Definitions occuring in Statement :  ctt_meaning: [[ctxt;t]] ctt-term: CttTerm ctt-kind: ctt-kind(t) context-set: context-set(ctxt) context-ok: context-ok(ctxt) cubical-context: ?CubicalContext ctt-type-meaning: cttType(X) uimplies: supposing a subtype_rel: A ⊆B uall: [x:A]. B[x] all: x:A. B[x] natural_number: $n int: equal: t ∈ T provisional-type: Provisional(T)
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a all: x:A. B[x] subtype_rel: A ⊆B ctt-term: CttTerm wfterm: wfterm(opr;sort;arity) nat: so_lambda: λ2x.t[x] so_apply: x[s] ctt-is-fibrant: ctt-is-fibrant(t) ctt-kind: ctt-kind(t) implies:  Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) and: P ∧ Q ifthenelse: if then else fi  bnot: ¬bb bfalse: ff band: p ∧b q assert: b false: False sq_type: SQType(T) guard: {T} true: True exists: x:A. B[x] or: P ∨ Q sq_stable: SqStable(P) squash: T iff: ⇐⇒ Q eq_atom: =a y
Lemmas referenced :  assert-ctt-is-fibrant istype-int ctt-kind_wf set_subtype_base le_wf int_subtype_base ctt-term_wf isvarterm_wf ctt-op_wf eqtt_to_assert subtype_base_sq eqff_to_assert bool_cases_sqequal bool_wf bool_subtype_base assert-bnot ctt-op-sort_wf term-opr_wf sq_stable__l_member decidable__atom_equal cons_wf nil_wf cons_member atom_subtype_base member_singleton
Rules used in proof :  cut introduction extract_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt hypothesis sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination sqequalRule lambdaEquality_alt dependent_functionElimination isect_memberEquality_alt axiomEquality isectIsTypeImplies inhabitedIsType functionIsTypeImplies equalityIstype setElimination rename applyEquality intEquality natural_numberEquality baseClosed sqequalBase equalitySymmetry universeIsType instantiate lambdaFormation_alt unionElimination equalityElimination equalityTransitivity productElimination cumulativity independent_functionElimination voidElimination dependent_pairFormation_alt promote_hyp because_Cache atomEquality tokenEquality imageMemberEquality imageElimination

Latex:
\mforall{}[t:CttTerm]
    \mforall{}X:?CubicalContext.  [[X;t]]  \msubseteq{}r  Provisional''''(cttType(context-set(X)))  supposing  context-ok(X) 
    supposing  ctt-kind(t)  =  1



Date html generated: 2020_05_21-AM-10_36_33
Last ObjectModification: 2020_05_05-AM-10_47_09

Theory : cubical!type!theory


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