Nuprl Lemma : update-context3_wf
∀[X:?CubicalContext]
∀[v:varname()]. ∀[t:Provisional''''(cttTerm(context-set(X)))]. (update-context3(X;v;t) ∈ ?CubicalContext)
supposing context-ok(X)
Proof
Definitions occuring in Statement :
update-context3: update-context3(X;v;t),
context-set: context-set(ctxt),
context-ok: context-ok(ctxt),
cubical-context: ?CubicalContext,
ctt-term-meaning: cttTerm(X),
varname: varname(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
provisional-type: Provisional(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
cubical-context: ?CubicalContext,
update-context3: update-context3(X;v;t),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
cubical_context: CubicalContext,
context-set: context-set(ctxt),
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
context-set_wf,
provisional-type_wf,
ctt-term-meaning_wf,
varname_wf,
context-ok_wf,
cubical-context_wf,
cubical_context_wf,
update-cubical-context2_wf,
provisional-subtype,
ctt-type-meaning1_wf,
pi1_wf_top,
cubical_set_wf,
subtype_rel_self,
ctt-term-meaning-subtype2,
allowed_wf,
allow_wf,
bind-provision_wf,
subtype_rel_wf,
squash_wf,
true_wf,
istype-universe,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
universeIsType,
instantiate,
cumulativity,
setElimination,
rename,
productElimination,
applyEquality,
independent_pairEquality,
Error :memTop,
applyLambdaEquality,
sqequalRule,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
setIsType,
because_Cache,
productIsType,
equalityIstype,
lambdaEquality_alt,
imageElimination,
inhabitedIsType,
universeEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[X:?CubicalContext]
\mforall{}[v:varname()]. \mforall{}[t:Provisional''''(cttTerm(context-set(X)))].
(update-context3(X;v;t) \mmember{} ?CubicalContext)
supposing context-ok(X)
Date html generated:
2020_05_20-PM-08_14_01
Last ObjectModification:
2020_05_18-AM-09_29_53
Theory : cubical!type!theory
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